1 Simulating data

This section fits a population model of the theoretical phenomenon that are involved in the reward processing construct. The idea is that there are approach and avoidance (measured phenomena) characteristics that are associated with stimuli within/across tasks. There is no ground truth of these processes at the individual. Nevertheless, the phenomena are important to the broad construct of reward processing, which within the MID task are hypothesized to reflect the the multidimensional affective circumplex model. As formalized here, in the MID task the contrasts reflect the phenomenon (i.e., reflective model) as opposed of the other way, whereby the items form the phenomenon (i.e., formativefmodel).

1.1 Specify Population Model

Start off by specifying the population model. In this scenario, the individual runs load onto the specific Contrast and ROI combinations. Then, the ROIs are loaded onto the factors approach and avoidance. The approach and avoidance are specified as negatively correlated and the factor variances are fixed to 1.

population_model<-'
# By run loadings for bilateral regions
AWin_v_Neut_L_NAcc =~     .7*AWin_v_Neut_L_NAcc_run1    + .7*AWin_v_Neut_L_NAcc_run2
AWin_v_Neut_L_Insula =~   .7*AWin_v_Neut_L_Insula_run1  + .7*AWin_v_Neut_L_Insula_run2
BWin_v_Neut_L_NAcc =~     .7*BWin_v_Neut_L_NAcc_run1    + .7*BWin_v_Neut_L_NAcc_run2
BWin_v_Neut_L_Insula =~   .7*BWin_v_Neut_L_Insula_run1  + .7*BWin_v_Neut_L_Insula_run2
BWin_v_BLose_L_NAcc =~    .7*BWin_v_BLose_L_NAcc_run1   + .7*BWin_v_BLose_L_NAcc_run2
BWin_v_BLose_L_Insula =~  .7*BWin_v_BLose_L_Insula_run1 + .7*BWin_v_BLose_L_Insula_run2
ALose_v_Neut_L_NAcc =~    .7*ALose_v_Neut_L_NAcc_run1   + .7*ALose_v_Neut_L_NAcc_run2
ALose_v_Neut_L_Insula =~  .7*ALose_v_Neut_L_Insula_run1 + .7*ALose_v_Neut_L_Insula_run2
BLose_v_Neut_L_NAcc =~    .7*BLose_v_Neut_L_NAcc_run1   + .7*BLose_v_Neut_L_NAcc_run2
BLose_v_Neut_L_Insula =~  .7*BLose_v_Neut_L_Insula_run1 + .7*BLose_v_Neut_L_Insula_run2
BLose_v_BWin_L_NAcc =~    .7*BLose_v_BWin_L_NAcc_run1   + .7*BLose_v_BWin_L_NAcc_run2
BLose_v_BWin_L_Insula =~  .7*BLose_v_BWin_L_Insula_run1 + .7*BLose_v_BWin_L_Insula_run2

AWin_v_Neut_R_NAcc =~     .7*AWin_v_Neut_R_NAcc_run1    + .7*AWin_v_Neut_R_NAcc_run2
AWin_v_Neut_R_Insula =~   .7*AWin_v_Neut_R_Insula_run1  + .7*AWin_v_Neut_R_Insula_run2
BWin_v_Neut_R_NAcc =~     .7*BWin_v_Neut_R_NAcc_run1    + .7*BWin_v_Neut_R_NAcc_run2
BWin_v_Neut_R_Insula =~   .7*BWin_v_Neut_R_Insula_run1  + .7*BWin_v_Neut_R_Insula_run2
BWin_v_BLose_R_NAcc =~    .7*BWin_v_BLose_R_NAcc_run1   + .7*BWin_v_BLose_R_NAcc_run2
BWin_v_BLose_R_Insula =~  .7*BWin_v_BLose_R_Insula_run1 + .7*BWin_v_BLose_R_Insula_run2
ALose_v_Neut_R_NAcc =~    .7*ALose_v_Neut_R_NAcc_run1   + .7*ALose_v_Neut_R_NAcc_run2
ALose_v_Neut_R_Insula =~  .7*ALose_v_Neut_R_Insula_run1 + .7*ALose_v_Neut_R_Insula_run2
BLose_v_Neut_R_NAcc =~    .7*BLose_v_Neut_R_NAcc_run1   + .7*BLose_v_Neut_R_NAcc_run2
BLose_v_Neut_R_Insula =~  .7*BLose_v_Neut_R_Insula_run1 + .7*BLose_v_Neut_R_Insula_run2
BLose_v_BWin_R_NAcc =~    .7*BLose_v_BWin_R_NAcc_run1   + .7*BLose_v_BWin_R_NAcc_run2
BLose_v_BWin_R_Insula =~  .7*BLose_v_BWin_R_Insula_run1 + .7*BLose_v_BWin_R_Insula_run2

#Factor item loadings 
Approach =~  .8*AWin_v_Neut_L_NAcc + .8*AWin_v_Neut_R_NAcc + .45*AWin_v_Neut_R_Insula +
            .7*BWin_v_Neut_L_NAcc +   .7*BWin_v_Neut_R_NAcc + .4*BWin_v_Neut_R_Insula +
            .8*BWin_v_BLose_L_NAcc +  .8*BWin_v_BLose_R_NAcc
                
Avoid =~  .8*ALose_v_Neut_L_Insula  + .8*ALose_v_Neut_R_Insula +
          .75*BLose_v_Neut_L_Insula + .75*BLose_v_Neut_R_Insula +
          .8*BLose_v_BWin_L_Insula  + .45*BLose_v_BWin_R_Insula
            
# Factor Covariances 
Approach ~~ -.6*Avoid

# Fixing factor variances
Approach ~~ 1*Approach
Avoid ~~ 1*Avoid

# Factor means/intercepts
#Approach ~ 1
#Avoid ~ 1
'

1.2 General samples

Using the population model, simsem is used to create simulated data based on the population model. This generates a fake dataset that is used to pilot the planned CFA, ESEM, EFA and Local SEM models

In this case, 50 repetitions are simulated per model for an approximate N sample for each study. Even though the factor variances are specified in the population model as ‘1’, this model fixeds all latent variables using std.lv = TRUE.

  1. AHRB N = 104
  2. MLS N = 120
  3. ABCD N = 1000
# Using simsem to fit population model by creating a simulated set of 50 population sets. Do this for a dummy AHRB, MLS and ABCD sample
# the samples size is mean to be comparable to what I'd estimate I'd have access to in the real data.
set.seed(25151215)
sim_AHRB <- simsem::sim(nRep = 50, model = "lavaan", n = 104, 
           generate = population_model, std.lv = TRUE, lavaanfun = "sem", 
           # std.lv ~ ix the variances of all the latent variables 
           dataOnly=T, meanstructure = FALSE, seed=123)

sim_MLS <- simsem::sim(nRep = 50, model = "lavaan", n = 120, 
                generate = population_model, std.lv = TRUE, lavaanfun = "sem", 
                dataOnly=T, meanstructure = FALSE, seed=123)

sim_ABCD <- simsem::sim(nRep = 50, model = "lavaan", n = 1000, 
               generate = population_model, std.lv = TRUE, lavaanfun = "sem", 
               dataOnly=T, meanstructure = FALSE, seed=123)

Average each repeptition for sample simulated. For example, after 50 repitions of 1000 participants for the population model of ABCD sample, an average estimate is derived using aaply. For each study, the set variable is created to differentiate which sample the data is associated with (i.e., grouping variable).

# for each simulate sets (50) of data, taking the mean of sets to create final study specific datasets, AHRB (3), MLS (2), ABCD (1)
sim_AHRB_data <- data.frame(aaply(laply(sim_AHRB, as.matrix), c(2,3), mean))
  sim_AHRB_data$set <-3
  
sim_MLS_data <- data.frame(aaply(laply(sim_MLS, as.matrix), c(2,3), mean))
  sim_MLS_data$set <-2
  
sim_ABCD_data <- data.frame(aaply(laply(sim_ABCD, as.matrix), c(2,3), mean))
  sim_ABCD_data$set <-1

Next, row bind the data sets to form one complete data

#Combining the dataset to create a 2259 (combined participants) x 25 (variables)
brain_set <- rbind(sim_AHRB_data,sim_MLS_data,sim_ABCD_data)

1.3 Correlation matrix of data

Here, a combination of rcorr and corrplot is used visualize the data.

# Using Hmisc to create a 24x24 matrix for a list (3) that contains: the pearson's r corr, sample size (N), and significance (p).
Brain_corr = rcorr(as.matrix(subset(brain_set,select=-c(set))), # excluding the set of data related to sample
                   type = "pearson")


# Using corrplot() to create heatmap of the data. 
par(mfrow=c(1,1))
corrplot(Brain_corr$r, type = "upper", 
         order = 'hclust',
         method =  "color", 
         tl.cex = 0.5, tl.col = 'black',
         cl.pos = 'r', tl.pos = 'lt', outline = TRUE,
         col=colorRampPalette(c("navyblue","white","red2"))(100),# colours http://www.stat.columbia.edu/~tzheng/files/Rcolor.pdf
         mar = c(2,.15,.25,.15)#bottom, left, top and right,
         )



2 Running [restricted] CFA + Multigroup CFA

Run the CFA multi-group analysis for the three datasets. Multi-group CFA tests the measurement invariance across defined groups to determine whether soft and strict invariance criteria are met and the degree to which the derive estimates for an item in one study can be compared to the same item in another sample. In this case, the focus is on the configural (structure) and metric invariance (loadings). In short, this model evalutes whether factor structure and loadings for the approach and avoidance model are invariant (dont significant differ) across the samples.

Code here is based on measurement invariance models from Maasen et al. 2019, Measurement invariance presentation from Kate Xu and Multi-group CFA tutorial from Hirschfeld & Brachel (2014).

The issue of multi-group is invariance what is discussed in Borsboom (2006). In short, (1) Interpretation of group differences on observed scores DEPENDS on the invariance of measurement models & (2) many make conclusions without doing a single test of measurement invariance.

2.1 Not used CFA Model

The initial idea was to fit values from each run (e.g., run 1 and run 2 for RightNACC_Contrast1) onto a single indicator (i.e., RightNAcc_Contrast1) to account for reliability across runs. However, the run data often consist of lower ICC values and so the model may have trouble converging. This method will also create a path-to-sample ratio of 1 to <=3. This is pretty low and may produce unreliable estimates in the maximum likelihood framework (even if using robust estimate) (see Kline 2015 book on Principles and Practice of Structural Equation Modeling)

Below is an example of a model that will not be used due to smaller N but may be in future large N samples.

MID_model_notused <-'
# Run Loadings
# To impose equality contraints across runs? Too many runs to estimates with to few data? Not using here at this time
 AWin_v_Neut_R_NAcc    =~  AWin_v_Neut_R_NAcc_run1   + AWin_v_Neut_R_NAcc_run2
 AWin_v_Neut_R_Insula  =~  AWin_v_Neut_R_Insula_run1 + AWin_v_Neut_R_Insula_run2
 BWin_v_Neut_R_NAcc    =~  BWin_v_Neut_R_NAcc_run1   + BWin_v_Neut_R_NAcc_run2
 BWin_v_Neut_R_Insula  =~  BWin_v_Neut_R_Insula_run1 + BWin_v_Neut_R_Insula_run2
 BWin_v_BLose_R_NAcc   =~  BWin_v_BLose_R_NAcc_run1  + BWin_v_BLose_R_NAcc_run2
 BWin_v_BLose_R_Insula  =~ BWin_v_BLose_R_Insula_run1+ BWin_v_BLose_R_Insula_run2
 ALose_v_Neut_R_NAcc   =~  ALose_v_Neut_R_NAcc_run1  + ALose_v_Neut_R_NAcc_run2
 ALose_v_Neut_R_Insula =~  ALose_v_Neut_R_Insula_run1+ ALose_v_Neut_R_Insula_run2  
 BLose_v_Neut_R_NAcc   =~  BLose_v_Neut_R_NAcc_run1  + BLose_v_Neut_R_NAcc_run2
 BLose_v_Neut_R_Insula =~  BLose_v_Neut_R_Insula_run1+ BLose_v_Neut_R_Insula_run2
 BLose_v_BWin_R_NAcc   =~  BLose_v_BWin_R_NAcc_run1  + BLose_v_BWin_R_NAcc_run2
 BLose_v_BWin_R_Insula =~  BLose_v_BWin_R_Insula_run1+ BLose_v_BWin_R_Insula_run2
 
# Using [m-x] to impose simple equality constraints on individual runs loading onto avg run values
 AWin_v_Neut_L_NAcc    =~  AWin_v_Neut_L_NAcc_run1   + AWin_v_Neut_L_NAcc_run2
 AWin_v_Neut_L_Insula  =~  AWin_v_Neut_L_Insula_run1 + AWin_v_Neut_L_Insula_run2
 BWin_v_Neut_L_NAcc    =~  BWin_v_Neut_L_NAcc_run1   + BWin_v_Neut_L_NAcc_run2
 BWin_v_Neut_L_Insula  =~  BWin_v_Neut_L_Insula_run1 + BWin_v_Neut_L_Insula_run2
 BWin_v_BLose_L_NAcc   =~  BWin_v_BLose_L_NAcc_run1  + BWin_v_BLose_L_NAcc_run2
 BWin_v_BLose_L_Insula  =~ BWin_v_BLose_L_Insula_run1+ BWin_v_BLose_L_Insula_run2
 ALose_v_Neut_L_NAcc   =~  ALose_v_Neut_L_NAcc_run1  + ALose_v_Neut_L_NAcc_run2
 ALose_v_Neut_L_Insula =~  ALose_v_Neut_L_Insula_run1+ ALose_v_Neut_L_Insula_run2  
 BLose_v_Neut_L_NAcc   =~  BLose_v_Neut_L_NAcc_run1  + BLose_v_Neut_L_NAcc_run2
 BLose_v_Neut_L_Insula =~  BLose_v_Neut_L_Insula_run1+ BLose_v_Neut_L_Insula_run2
 BLose_v_BWin_L_NAcc   =~  BLose_v_BWin_L_NAcc_run1  + BLose_v_BWin_L_NAcc_run2
 BLose_v_BWin_L_Insula =~  BLose_v_BWin_L_Insula_run1+ BLose_v_BWin_L_Insula_run2
 

Approach =~ AWin_v_Neut_L_NAcc  + AWin_v_Neut_R_NAcc  + AWin_v_Neut_R_Insula +
            BWin_v_Neut_L_NAcc  + BWin_v_Neut_R_NAcc  + BWin_v_Neut_R_Insula +
            BWin_v_BLose_L_NAcc + BWin_v_BLose_R_NAcc  
                
Avoid =~    ALose_v_Neut_L_Insula + ALose_v_Neut_L_Insula +
            BLose_v_Neut_L_Insula + BLose_v_Neut_R_Insula +
            BLose_v_BWin_L_Insula + BLose_v_BWin_R_Insula 
'

2.2 Used CFA model

The below specified model will be used. The number of estimate parameters are fewer and may be more appropriate for the theoretical model. This model may result in few convergence issues if the number of participants ends up to be few and the coefficients/estimates are lower.

MID_model <-'

# Factor loadings
Approach =~ AWin_v_Neut_L_NAcc_run1  + AWin_v_Neut_R_NAcc_run1  + AWin_v_Neut_R_Insula_run1 +
            BWin_v_Neut_L_NAcc_run1  + BWin_v_Neut_R_NAcc_run1  + BWin_v_Neut_R_Insula_run1 +
            BWin_v_BLose_L_NAcc_run1 + BWin_v_BLose_R_NAcc_run1 +
            AWin_v_Neut_L_NAcc_run2  + AWin_v_Neut_R_NAcc_run2 + AWin_v_Neut_R_Insula_run2 +
            BWin_v_Neut_L_NAcc_run2  + BWin_v_Neut_R_NAcc_run2  + BWin_v_Neut_R_Insula_run2 +
            BWin_v_BLose_L_NAcc_run2 + BWin_v_BLose_R_NAcc_run2 
                
Avoid =~    ALose_v_Neut_L_Insula_run1 + ALose_v_Neut_L_Insula_run1 +
            BLose_v_Neut_L_Insula_run1 + BLose_v_Neut_R_Insula_run1 +
            BLose_v_BWin_L_Insula_run1 + BLose_v_BWin_R_Insula_run1 +
            ALose_v_Neut_L_Insula_run2 + ALose_v_Neut_R_Insula_run2 +
            BLose_v_Neut_L_Insula_run2 + BLose_v_Neut_R_Insula_run2 +
            BLose_v_BWin_L_Insula_run2 + BLose_v_BWin_R_Insula_run2 
'

2.3 Running CFA: Three Samples

Below is the CFA model that is used to test the proposed restricted model (see Figure 1 in the manuscript). The CFA fitting procedure is consistent with the description here. For each CFA model, the full sample is filtered for each type sample, e.g. AHRB, MLS, ABCD. The std.lv= = TRUE constrain the latent factor variances to 1. The estimator being used is MLR, a maximum likelihood robust estimator. In addition to a model for each sample, a CFA model is estimated for the complete data (i.e., all three datasets).

# For starters, the CFA is estimated for each sample that is simulated (i.e., AHRB [1], MLS [2], ABCD [3])
AHRB_cfa <- cfa(model = MID_model, data = subset(brain_set %>% filter(set==3)),
                estimator = "MLR", std.lv = TRUE, meanstructure = TRUE) # fixing latent variances to 1
MLS_cfa <- cfa(model = MID_model, data = subset(brain_set %>% filter(set==2)),
               estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)
ABCD_cfa <- cfa(model = MID_model, data = subset(brain_set %>% filter(set==1)),
                estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

all_cfa <- cfa(model = MID_model, data = brain_set,
               estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

2.4 Fitting Configural CFA

Here, the configular multigroup model is fit. As described in D’Urso et al. (2022) measurement invariance pre-print, the configural model tests:

is the structure of the factors is invariannt across the samples (‘set’). In other words, if we a priori propose a two-factor structure (FA 1 = approch and FA 2 = Avoidance), does this two factor structure represent the between-person variability in the items that reflect the factors across each sample?

If the variability in one sample suggests a one, three, or four factor structure, this will be degrade the fit statistics.

A pre-specified CFA model is used to evaluate whether the measures/items that reflect the factor are the same across groups. group= 'set' is used to define the grouping variable. All loadings and intercepts are free to vary across groups, and the factor variance is set to ‘1’ via std.lv = TRUE

configural_cfa <- cfa(model = MID_model, data = brain_set, group = 'set', 
                      estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

2.5 Fitting Metric CFA

After fitting the CFA configurial (factor structure) invariance, if the model fit is not poor, then the next step is to test the metric invariance. Metric invariance tests:

are the loadings are consistent across the groups. In other words,are the phenomena (i.e., approach and avoidance) reflected by the same pattern across the measures/items?

One cause for concern may be that the phenomenon are not invariant across age groups, in that the items/measures (ROIs for a given contrast) do not load in the same manner onto each factor. This ‘soft’ measure of invariance can determine whether the items functions differ across the items and so cannot be easily compared.

The model is fit using the same procedure as for configurial invariance with one exception: In metric invariance the loadings group equality constraint is added to the model via group.equal=c("loadings"). The model fit statistics are used to evaluate whether the fit is poor.

metric_cfa <-cfa(model = MID_model, data = brain_set, 
                 group = 'set', group.equal=c("loadings"),
                 estimator = "MLR", std.lv = TRUE, meanstructure = TRUE)

2.6 Extracting Fit Statistics

Once the above models are fit, the following information is pulled out and saved into a out data frame:

  1. Model name
  2. Chi-square statistics
  3. Model Degrees of Freedom (df)
  4. Model p-value
  5. RMSEA
  6. CFI
  7. SRMR
  8. AIC
  9. BIC
# Below selects specific fit data as described in Maassen et al. 2019 OSF. No comparisons are made to compare models at this point.
out <- matrix(NA, ncol = 9, nrow = 7)
colnames(out) <- c("model","chisq","df","pvalue", "rmsea", "cfi", "srmr",
                   "AIC", "BIC")

# save fit measures from models
out[1,2:7] <- round(data.matrix(fitmeasures(AHRB_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)

out[2,2:7] <- round(data.matrix(fitmeasures(MLS_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)

out[3,2:7] <- round(data.matrix(fitmeasures(ABCD_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)

out[4,2:7] <- round(data.matrix(fitmeasures(all_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)

out[5,2:7] <- round(data.matrix(fitmeasures(configural_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                            digits=3)

out[6,2:7] <- round(data.matrix(fitmeasures(metric_cfa, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)


# AIC models
out[1,8] <- round(AIC(AHRB_cfa),3)
out[2,8] <- round(AIC(MLS_cfa),3)
out[3,8] <- round(AIC(ABCD_cfa),3)
out[4,8] <- round(AIC(all_cfa),3)
out[5,8] <- round(AIC(configural_cfa),3)
out[6,8] <- round(AIC(metric_cfa),3)

# BIC models
out[1,9] <- round(BIC(AHRB_cfa),3)
out[2,9] <- round(BIC(MLS_cfa),3)
out[3,9] <- round(BIC(ABCD_cfa),3)
out[4,9] <- round(BIC(all_cfa),3)
out[5,9] <- round(BIC(configural_cfa),3)
out[6,9] <- round(BIC(metric_cfa),3)

out[1:6,1] <-  c("AHRB CFA","MLS CFA","ABCD CFA", "Overall CFA", "Configg MG-CFA", "Metric MG-CFA")

2.7 Model Parameter Summary

Reporting standardized coefficients.

2.7.1 AHRB CFA model

##### Summarizing CFA models #####
parameters(AHRB_cfa, standardize = T)
## # Loading
## 
## Link                                  | Coefficient |   SE |        95% CI |    z |      p
## ------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.48 | 0.13 | [ 0.23, 0.73] | 3.81 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.45 | 0.10 | [ 0.26, 0.65] | 4.59 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.33 | 0.11 | [ 0.11, 0.56] | 2.90 | 0.004 
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.29 | 0.12 | [ 0.04, 0.53] | 2.31 | 0.021 
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.49 | 0.14 | [ 0.21, 0.77] | 3.45 | < .001
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.26 | 0.11 | [ 0.05, 0.47] | 2.42 | 0.016 
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.33 | 0.11 | [ 0.12, 0.53] | 3.10 | 0.002 
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.48 | 0.15 | [ 0.19, 0.77] | 3.26 | 0.001 
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.67 | 0.13 | [ 0.42, 0.93] | 5.13 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.41 | 0.11 | [ 0.20, 0.62] | 3.78 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.31 | 0.14 | [ 0.03, 0.58] | 2.18 | 0.029 
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.19 | 0.13 | [-0.08, 0.45] | 1.39 | 0.163 
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.55 | 0.13 | [ 0.31, 0.80] | 4.38 | < .001
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.12 | 0.13 | [-0.14, 0.37] | 0.91 | 0.365 
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.28 | 0.10 | [ 0.09, 0.47] | 2.87 | 0.004 
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.55 | 0.14 | [ 0.28, 0.82] | 4.03 | < .001
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.33 | 0.14 | [ 0.05, 0.61] | 2.30 | 0.021 
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.65 | 0.09 | [ 0.47, 0.83] | 7.04 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.43 | 0.11 | [ 0.21, 0.65] | 3.86 | < .001
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.46 | 0.12 | [ 0.23, 0.69] | 3.91 | < .001
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.28 | 0.11 | [ 0.06, 0.50] | 2.49 | 0.013 
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.37 | 0.12 | [ 0.14, 0.60] | 3.12 | 0.002 
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.41 | 0.09 | [ 0.23, 0.59] | 4.41 | < .001
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.65 | 0.08 | [ 0.50, 0.81] | 8.38 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.40 | 0.12 | [ 0.15, 0.64] | 3.21 | 0.001 
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.38 | 0.11 | [ 0.15, 0.60] | 3.28 | 0.001 
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.27 | 0.10 | [ 0.08, 0.46] | 2.81 | 0.005 
## 
## # Correlation
## 
## Link              | Coefficient |   SE |        95% CI |     z |     p
## ----------------------------------------------------------------------
## Approach ~~ Avoid |       -0.29 | 0.16 | [-0.60, 0.02] | -1.81 | 0.070

2.7.2 MLS CFA model

##### Summarizing CFA models #####
parameters(MLS_cfa, standardize = T)
## # Loading
## 
## Link                                  | Coefficient |   SE |        95% CI |    z |      p
## ------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.46 | 0.14 | [ 0.18, 0.73] | 3.28 | 0.001 
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.44 | 0.15 | [ 0.14, 0.74] | 2.88 | 0.004 
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.10 | 0.13 | [-0.16, 0.35] | 0.75 | 0.455 
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.24 | 0.11 | [ 0.03, 0.45] | 2.28 | 0.022 
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.32 | 0.12 | [ 0.08, 0.56] | 2.65 | 0.008 
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.27 | 0.11 | [ 0.05, 0.50] | 2.43 | 0.015 
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.43 | 0.14 | [ 0.16, 0.70] | 3.17 | 0.002 
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.45 | 0.10 | [ 0.26, 0.64] | 4.56 | < .001
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.47 | 0.13 | [ 0.21, 0.73] | 3.59 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.57 | 0.13 | [ 0.32, 0.81] | 4.52 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.10 | 0.13 | [-0.16, 0.36] | 0.72 | 0.472 
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.25 | 0.13 | [-0.01, 0.51] | 1.87 | 0.061 
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.30 | 0.12 | [ 0.07, 0.54] | 2.54 | 0.011 
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.17 | 0.12 | [-0.06, 0.40] | 1.47 | 0.143 
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.46 | 0.12 | [ 0.23, 0.69] | 3.90 | < .001
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.25 | 0.12 | [ 0.01, 0.49] | 2.06 | 0.039 
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.65 | 0.18 | [ 0.30, 1.00] | 3.67 | < .001
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.28 | 0.10 | [ 0.09, 0.47] | 2.92 | 0.003 
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.26 | 0.16 | [-0.06, 0.58] | 1.58 | 0.115 
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.49 | 0.17 | [ 0.15, 0.83] | 2.80 | 0.005 
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.23 | 0.10 | [ 0.04, 0.43] | 2.33 | 0.020 
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.80 | 0.16 | [ 0.49, 1.11] | 5.00 | < .001
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.40 | 0.12 | [ 0.16, 0.65] | 3.22 | 0.001 
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.36 | 0.11 | [ 0.15, 0.56] | 3.36 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.42 | 0.14 | [ 0.13, 0.70] | 2.89 | 0.004 
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.54 | 0.15 | [ 0.24, 0.84] | 3.56 | < .001
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.25 | 0.10 | [ 0.06, 0.44] | 2.59 | 0.010 
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |     z |     p
## -----------------------------------------------------------------------
## Approach ~~ Avoid |       -0.36 | 0.17 | [-0.70, -0.02] | -2.10 | 0.036

2.7.3 ABCD CFA model

##### Summarizing CFA models #####
parameters(ABCD_cfa, standardize = T)
## # Loading
## 
## Link                                  | Coefficient |   SE |       95% CI |     z |      p
## ------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.45 | 0.03 | [0.38, 0.52] | 13.10 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.44 | 0.03 | [0.37, 0.50] | 13.45 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.24 | 0.04 | [0.17, 0.31] |  6.68 | < .001
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.51 | 0.03 | [0.45, 0.57] | 17.07 | < .001
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.39 | 0.03 | [0.32, 0.45] | 12.08 | < .001
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.24 | 0.03 | [0.17, 0.31] |  6.91 | < .001
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.47 | 0.03 | [0.41, 0.53] | 14.83 | < .001
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.46 | 0.03 | [0.40, 0.53] | 14.38 | < .001
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.48 | 0.03 | [0.42, 0.55] | 14.83 | < .001
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.50 | 0.03 | [0.44, 0.55] | 17.12 | < .001
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.27 | 0.03 | [0.20, 0.34] |  7.85 | < .001
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.42 | 0.03 | [0.36, 0.49] | 13.22 | < .001
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.42 | 0.03 | [0.36, 0.48] | 13.51 | < .001
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.27 | 0.04 | [0.20, 0.34] |  7.39 | < .001
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.42 | 0.03 | [0.35, 0.48] | 12.71 | < .001
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.48 | 0.03 | [0.42, 0.55] | 14.90 | < .001
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.46 | 0.04 | [0.39, 0.53] | 13.01 | < .001
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.46 | 0.04 | [0.39, 0.53] | 13.05 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.52 | 0.04 | [0.45, 0.59] | 14.55 | < .001
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.44 | 0.04 | [0.37, 0.51] | 12.02 | < .001
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.24 | 0.04 | [0.17, 0.32] |  6.39 | < .001
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.42 | 0.03 | [0.35, 0.48] | 12.33 | < .001
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.39 | 0.03 | [0.33, 0.45] | 12.27 | < .001
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.43 | 0.04 | [0.36, 0.50] | 11.63 | < .001
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.49 | 0.04 | [0.42, 0.56] | 13.99 | < .001
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.42 | 0.04 | [0.35, 0.49] | 11.31 | < .001
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.23 | 0.04 | [0.16, 0.31] |  6.05 | < .001
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |      z |      p
## -------------------------------------------------------------------------
## Approach ~~ Avoid |       -0.56 | 0.03 | [-0.63, -0.50] | -16.62 | < .001

2.7.4 Configural CFA model

##### Summarizing CFA models #####
parameters(configural_cfa, standardize = T)
## # Loading
## 
## Link                                  | Coefficient |   SE |        95% CI |     z |      p | Group
## ---------------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.48 | 0.13 | [ 0.23, 0.73] |  3.81 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.45 | 0.10 | [ 0.26, 0.65] |  4.59 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.33 | 0.11 | [ 0.11, 0.56] |  2.90 | 0.004  |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.29 | 0.12 | [ 0.04, 0.53] |  2.31 | 0.021  |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.49 | 0.14 | [ 0.21, 0.77] |  3.45 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.26 | 0.11 | [ 0.05, 0.47] |  2.42 | 0.016  |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.33 | 0.11 | [ 0.12, 0.53] |  3.10 | 0.002  |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.48 | 0.15 | [ 0.19, 0.77] |  3.26 | 0.001  |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.67 | 0.13 | [ 0.42, 0.93] |  5.13 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.41 | 0.11 | [ 0.20, 0.62] |  3.78 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.31 | 0.14 | [ 0.03, 0.58] |  2.18 | 0.029  |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.19 | 0.13 | [-0.08, 0.45] |  1.39 | 0.163  |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.55 | 0.13 | [ 0.31, 0.80] |  4.38 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.12 | 0.13 | [-0.14, 0.37] |  0.91 | 0.365  |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.28 | 0.10 | [ 0.09, 0.47] |  2.87 | 0.004  |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.55 | 0.14 | [ 0.28, 0.82] |  4.03 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.33 | 0.14 | [ 0.05, 0.61] |  2.30 | 0.021  |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.65 | 0.09 | [ 0.47, 0.83] |  7.04 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.43 | 0.11 | [ 0.21, 0.65] |  3.86 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.46 | 0.12 | [ 0.23, 0.69] |  3.91 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.28 | 0.11 | [ 0.06, 0.50] |  2.49 | 0.013  |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.37 | 0.12 | [ 0.14, 0.60] |  3.12 | 0.002  |  1.00
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.41 | 0.09 | [ 0.23, 0.59] |  4.41 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.65 | 0.08 | [ 0.50, 0.81] |  8.38 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.40 | 0.12 | [ 0.15, 0.64] |  3.21 | 0.001  |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.38 | 0.11 | [ 0.15, 0.60] |  3.28 | 0.001  |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.27 | 0.10 | [ 0.08, 0.46] |  2.81 | 0.005  |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.46 | 0.14 | [ 0.18, 0.73] |  3.28 | 0.001  |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.44 | 0.15 | [ 0.14, 0.74] |  2.88 | 0.004  |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.10 | 0.13 | [-0.16, 0.35] |  0.75 | 0.455  |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.24 | 0.11 | [ 0.03, 0.45] |  2.28 | 0.022  |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.32 | 0.12 | [ 0.08, 0.56] |  2.65 | 0.008  |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.27 | 0.11 | [ 0.05, 0.50] |  2.43 | 0.015  |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.43 | 0.14 | [ 0.16, 0.70] |  3.17 | 0.002  |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.45 | 0.10 | [ 0.26, 0.64] |  4.56 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.47 | 0.13 | [ 0.21, 0.73] |  3.59 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.57 | 0.13 | [ 0.32, 0.81] |  4.52 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.10 | 0.13 | [-0.16, 0.36] |  0.72 | 0.472  |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.25 | 0.13 | [-0.01, 0.51] |  1.87 | 0.061  |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.30 | 0.12 | [ 0.07, 0.54] |  2.54 | 0.011  |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.17 | 0.12 | [-0.06, 0.40] |  1.47 | 0.143  |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.46 | 0.12 | [ 0.23, 0.69] |  3.90 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.25 | 0.12 | [ 0.01, 0.49] |  2.06 | 0.039  |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.65 | 0.18 | [ 0.30, 1.00] |  3.67 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.28 | 0.10 | [ 0.09, 0.47] |  2.92 | 0.003  |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.26 | 0.16 | [-0.06, 0.58] |  1.58 | 0.115  |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.49 | 0.17 | [ 0.15, 0.83] |  2.80 | 0.005  |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.23 | 0.10 | [ 0.04, 0.43] |  2.33 | 0.020  |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.80 | 0.16 | [ 0.49, 1.11] |  5.00 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.40 | 0.12 | [ 0.16, 0.65] |  3.22 | 0.001  |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.36 | 0.11 | [ 0.15, 0.56] |  3.36 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.42 | 0.14 | [ 0.13, 0.70] |  2.89 | 0.004  |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.54 | 0.15 | [ 0.24, 0.84] |  3.56 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.25 | 0.10 | [ 0.06, 0.44] |  2.59 | 0.010  |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run1   |        0.45 | 0.03 | [ 0.38, 0.52] | 13.10 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run1   |        0.44 | 0.03 | [ 0.37, 0.50] | 13.45 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run1 |        0.24 | 0.04 | [ 0.17, 0.31] |  6.68 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run1   |        0.51 | 0.03 | [ 0.45, 0.57] | 17.07 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run1   |        0.39 | 0.03 | [ 0.32, 0.45] | 12.08 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run1 |        0.24 | 0.03 | [ 0.17, 0.31] |  6.91 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run1  |        0.47 | 0.03 | [ 0.41, 0.53] | 14.83 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run1  |        0.46 | 0.03 | [ 0.40, 0.53] | 14.38 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAcc_run2   |        0.48 | 0.03 | [ 0.42, 0.55] | 14.83 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run2   |        0.50 | 0.03 | [ 0.44, 0.55] | 17.12 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run2 |        0.27 | 0.03 | [ 0.20, 0.34] |  7.85 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run2   |        0.42 | 0.03 | [ 0.36, 0.49] | 13.22 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run2   |        0.42 | 0.03 | [ 0.36, 0.48] | 13.51 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run2 |        0.27 | 0.04 | [ 0.20, 0.34] |  7.39 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run2  |        0.42 | 0.03 | [ 0.35, 0.48] | 12.71 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run2  |        0.48 | 0.03 | [ 0.42, 0.55] | 14.90 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run1   |        0.46 | 0.04 | [ 0.39, 0.53] | 13.01 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run1   |        0.46 | 0.04 | [ 0.39, 0.53] | 13.05 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run1   |        0.52 | 0.04 | [ 0.45, 0.59] | 14.55 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run1   |        0.44 | 0.04 | [ 0.37, 0.51] | 12.02 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run1   |        0.24 | 0.04 | [ 0.17, 0.32] |  6.39 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run2   |        0.42 | 0.03 | [ 0.35, 0.48] | 12.33 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Insula_run2   |        0.39 | 0.03 | [ 0.33, 0.45] | 12.27 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run2   |        0.43 | 0.04 | [ 0.36, 0.50] | 11.63 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run2   |        0.49 | 0.04 | [ 0.42, 0.56] | 13.99 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run2   |        0.42 | 0.04 | [ 0.35, 0.49] | 11.31 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run2   |        0.23 | 0.04 | [ 0.16, 0.31] |  6.05 | < .001 |  3.00
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |      z |      p | Group
## ---------------------------------------------------------------------------------
## Approach ~~ Avoid |       -0.29 | 0.16 | [-0.60,  0.02] |  -1.81 | 0.070  |  1.00
## Approach ~~ Avoid |       -0.36 | 0.17 | [-0.70, -0.02] |  -2.10 | 0.036  |  2.00
## Approach ~~ Avoid |       -0.56 | 0.03 | [-0.63, -0.50] | -16.62 | < .001 |  3.00

2.7.5 Metric CFA model

##### Summarizing CFA models #####
parameters(metric_cfa, standardize = T)
## # Loading
## 
## Link                                          | Coefficient |   SE |       95% CI |     z |      p | Group
## ----------------------------------------------------------------------------------------------------------
## Approach =~ AWin_v_Neut_L_NAcc_run1 (.p1.)    |        0.42 | 0.05 | [0.32, 0.53] |  8.02 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run1 (.p2.)    |        0.45 | 0.06 | [0.33, 0.56] |  7.57 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run1 (.p3.)  |        0.23 | 0.04 | [0.14, 0.31] |  5.29 | < .001 |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run1 (.p4.)    |        0.43 | 0.05 | [0.34, 0.52] |  9.39 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run1 (.p5.)    |        0.40 | 0.06 | [0.28, 0.51] |  7.00 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run1 (.p6.)  |        0.26 | 0.05 | [0.17, 0.35] |  5.71 | < .001 |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run1 (.p7.)   |        0.43 | 0.05 | [0.32, 0.53] |  7.98 | < .001 |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run1 (.p8.)   |        0.45 | 0.06 | [0.35, 0.56] |  8.15 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run2 (.p9.)    |        0.55 | 0.06 | [0.43, 0.68] |  8.73 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_NAcc_run2 (.p10.)   |        0.48 | 0.05 | [0.38, 0.58] |  9.57 | < .001 |  1.00
## Approach =~ AWin_v_Neut_R_Insula_run2 (.p11.) |        0.26 | 0.04 | [0.17, 0.35] |  5.88 | < .001 |  1.00
## Approach =~ BWin_v_Neut_L_NAcc_run2 (.p12.)   |        0.38 | 0.04 | [0.30, 0.47] |  8.57 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_NAcc_run2 (.p13.)   |        0.41 | 0.06 | [0.30, 0.52] |  7.36 | < .001 |  1.00
## Approach =~ BWin_v_Neut_R_Insula_run2 (.p14.) |        0.29 | 0.04 | [0.20, 0.37] |  6.58 | < .001 |  1.00
## Approach =~ BWin_v_BLose_L_NAcc_run2 (.p15.)  |        0.38 | 0.05 | [0.28, 0.48] |  7.75 | < .001 |  1.00
## Approach =~ BWin_v_BLose_R_NAcc_run2 (.p16.)  |        0.48 | 0.05 | [0.38, 0.59] |  8.80 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run1 (.p17.)   |        0.46 | 0.05 | [0.36, 0.56] |  8.86 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run1 (.p18.)   |        0.46 | 0.06 | [0.34, 0.58] |  7.53 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run1 (.p19.)   |        0.48 | 0.06 | [0.37, 0.59] |  8.70 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run1 (.p20.)   |        0.50 | 0.06 | [0.38, 0.61] |  8.39 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run1 (.p21.)   |        0.26 | 0.05 | [0.16, 0.36] |  5.22 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_L_Insula_run2 (.p22.)   |        0.44 | 0.05 | [0.33, 0.54] |  8.14 | < .001 |  1.00
## Avoid =~ ALose_v_Neut_R_Insula_run2 (.p23.)   |        0.41 | 0.05 | [0.31, 0.50] |  8.13 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_L_Insula_run2 (.p24.)   |        0.51 | 0.06 | [0.38, 0.63] |  7.80 | < .001 |  1.00
## Avoid =~ BLose_v_Neut_R_Insula_run2 (.p25.)   |        0.48 | 0.06 | [0.38, 0.59] |  8.77 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_L_Insula_run2 (.p26.)   |        0.41 | 0.05 | [0.30, 0.51] |  7.42 | < .001 |  1.00
## Avoid =~ BLose_v_BWin_R_Insula_run2 (.p27.)   |        0.26 | 0.05 | [0.16, 0.35] |  5.33 | < .001 |  1.00
## Approach =~ AWin_v_Neut_L_NAcc_run1 (.p1.)    |        0.37 | 0.05 | [0.29, 0.46] |  8.25 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run1 (.p2.)    |        0.40 | 0.05 | [0.31, 0.50] |  8.22 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run1 (.p3.)  |        0.21 | 0.03 | [0.15, 0.28] |  6.28 | < .001 |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run1 (.p4.)    |        0.40 | 0.04 | [0.32, 0.47] | 10.12 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run1 (.p5.)    |        0.35 | 0.04 | [0.26, 0.43] |  8.41 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run1 (.p6.)  |        0.20 | 0.03 | [0.14, 0.27] |  5.98 | < .001 |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run1 (.p7.)   |        0.41 | 0.05 | [0.32, 0.49] |  8.99 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run1 (.p8.)   |        0.44 | 0.05 | [0.35, 0.52] |  9.63 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run2 (.p9.)    |        0.39 | 0.04 | [0.31, 0.48] |  9.16 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_NAcc_run2 (.p10.)   |        0.43 | 0.05 | [0.33, 0.52] |  8.63 | < .001 |  2.00
## Approach =~ AWin_v_Neut_R_Insula_run2 (.p11.) |        0.21 | 0.03 | [0.15, 0.28] |  6.38 | < .001 |  2.00
## Approach =~ BWin_v_Neut_L_NAcc_run2 (.p12.)   |        0.34 | 0.04 | [0.26, 0.41] |  8.59 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_NAcc_run2 (.p13.)   |        0.35 | 0.04 | [0.28, 0.43] |  9.44 | < .001 |  2.00
## Approach =~ BWin_v_Neut_R_Insula_run2 (.p14.) |        0.20 | 0.04 | [0.13, 0.27] |  5.72 | < .001 |  2.00
## Approach =~ BWin_v_BLose_L_NAcc_run2 (.p15.)  |        0.38 | 0.04 | [0.29, 0.47] |  8.52 | < .001 |  2.00
## Approach =~ BWin_v_BLose_R_NAcc_run2 (.p16.)  |        0.40 | 0.04 | [0.33, 0.48] | 10.49 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run1 (.p17.)   |        0.48 | 0.06 | [0.37, 0.59] |  8.71 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run1 (.p18.)   |        0.48 | 0.05 | [0.38, 0.57] | 10.13 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run1 (.p19.)   |        0.45 | 0.05 | [0.36, 0.55] |  9.80 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run1 (.p20.)   |        0.46 | 0.06 | [0.35, 0.57] |  8.21 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run1 (.p21.)   |        0.28 | 0.05 | [0.19, 0.37] |  6.04 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_L_Insula_run2 (.p22.)   |        0.54 | 0.07 | [0.41, 0.67] |  8.23 | < .001 |  2.00
## Avoid =~ ALose_v_Neut_R_Insula_run2 (.p23.)   |        0.43 | 0.05 | [0.32, 0.53] |  7.97 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_L_Insula_run2 (.p24.)   |        0.52 | 0.05 | [0.43, 0.62] | 10.78 | < .001 |  2.00
## Avoid =~ BLose_v_Neut_R_Insula_run2 (.p25.)   |        0.48 | 0.05 | [0.37, 0.58] |  8.85 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_L_Insula_run2 (.p26.)   |        0.48 | 0.06 | [0.36, 0.60] |  8.12 | < .001 |  2.00
## Avoid =~ BLose_v_BWin_R_Insula_run2 (.p27.)   |        0.23 | 0.04 | [0.15, 0.31] |  5.69 | < .001 |  2.00
## Approach =~ AWin_v_Neut_L_NAcc_run1 (.p1.)    |        0.46 | 0.03 | [0.40, 0.52] | 14.42 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run1 (.p2.)    |        0.44 | 0.03 | [0.39, 0.50] | 14.90 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run1 (.p3.)  |        0.24 | 0.03 | [0.17, 0.30] |  7.19 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run1 (.p4.)    |        0.48 | 0.03 | [0.42, 0.54] | 15.98 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run1 (.p5.)    |        0.39 | 0.03 | [0.33, 0.45] | 12.99 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run1 (.p6.)  |        0.24 | 0.03 | [0.18, 0.31] |  7.72 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run1 (.p7.)   |        0.47 | 0.03 | [0.41, 0.52] | 15.52 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run1 (.p8.)   |        0.47 | 0.03 | [0.41, 0.53] | 15.67 | < .001 |  3.00
## Approach =~ AWin_v_Neut_L_NAcc_run2 (.p9.)    |        0.50 | 0.03 | [0.44, 0.56] | 16.89 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_NAcc_run2 (.p10.)   |        0.50 | 0.03 | [0.45, 0.56] | 18.44 | < .001 |  3.00
## Approach =~ AWin_v_Neut_R_Insula_run2 (.p11.) |        0.27 | 0.03 | [0.20, 0.33] |  8.35 | < .001 |  3.00
## Approach =~ BWin_v_Neut_L_NAcc_run2 (.p12.)   |        0.40 | 0.03 | [0.33, 0.46] | 12.36 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_NAcc_run2 (.p13.)   |        0.43 | 0.03 | [0.37, 0.48] | 14.45 | < .001 |  3.00
## Approach =~ BWin_v_Neut_R_Insula_run2 (.p14.) |        0.25 | 0.04 | [0.18, 0.32] |  7.10 | < .001 |  3.00
## Approach =~ BWin_v_BLose_L_NAcc_run2 (.p15.)  |        0.42 | 0.03 | [0.35, 0.48] | 13.48 | < .001 |  3.00
## Approach =~ BWin_v_BLose_R_NAcc_run2 (.p16.)  |        0.48 | 0.03 | [0.42, 0.54] | 15.77 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run1 (.p17.)   |        0.46 | 0.03 | [0.39, 0.52] | 13.29 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run1 (.p18.)   |        0.45 | 0.03 | [0.39, 0.52] | 13.50 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run1 (.p19.)   |        0.50 | 0.03 | [0.43, 0.56] | 14.43 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run1 (.p20.)   |        0.45 | 0.03 | [0.39, 0.52] | 13.78 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run1 (.p21.)   |        0.24 | 0.03 | [0.18, 0.31] |  7.25 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_L_Insula_run2 (.p22.)   |        0.44 | 0.03 | [0.38, 0.50] | 14.36 | < .001 |  3.00
## Avoid =~ ALose_v_Neut_R_Insula_run2 (.p23.)   |        0.39 | 0.03 | [0.33, 0.45] | 13.57 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_L_Insula_run2 (.p24.)   |        0.43 | 0.03 | [0.36, 0.49] | 12.43 | < .001 |  3.00
## Avoid =~ BLose_v_Neut_R_Insula_run2 (.p25.)   |        0.48 | 0.03 | [0.42, 0.55] | 14.65 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_L_Insula_run2 (.p26.)   |        0.44 | 0.03 | [0.37, 0.50] | 13.26 | < .001 |  3.00
## Avoid =~ BLose_v_BWin_R_Insula_run2 (.p27.)   |        0.24 | 0.03 | [0.17, 0.30] |  6.94 | < .001 |  3.00
## 
## # Correlation
## 
## Link              | Coefficient |   SE |         95% CI |      z |      p | Group
## ---------------------------------------------------------------------------------
## Approach ~~ Avoid |       -0.32 | 0.12 | [-0.55, -0.09] |  -2.77 | 0.006  |  1.00
## Approach ~~ Avoid |       -0.41 | 0.11 | [-0.62, -0.19] |  -3.73 | < .001 |  2.00
## Approach ~~ Avoid |       -0.56 | 0.03 | [-0.63, -0.50] | -16.63 | < .001 |  3.00

2.8 Comparing models w/ BIC/AIC (anova)

The below compares whether the complete data (across all three samples) in the all_cfa model is significantly improved by the configural invariance model. A significant value indicates that the configural model is significantly better than the full sample cfa.

anova(all_cfa, configural_cfa)
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##                 Df    AIC    BIC  Chisq Chisq diff Df diff Pr(>Chisq)   
## all_cfa        323 -19878 -19459 1992.0                                 
## configural_cfa 969 -19740 -18483 2725.1     759.78     646   0.001285 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Next, anova is used to compare the model improve in AIC/BIC by between the configural and metric invariance. A significantly result in the anova would indicate a significant improvement of the metric model over the configural model.

anova(configural_cfa, metric_cfa)
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##                  Df    AIC    BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## configural_cfa  969 -19740 -18483 2725.1                              
## metric_cfa     1019 -19767 -18766 2797.8     58.114      50     0.2013

2.9 Plotting multi-group config. CFA

Use semPaths to plot the configural invariance CFA multigroup model

# this plottinig is not function with runs loading onto ROIs

layout(t(1:3))
semPaths(configural_cfa,
         color = "lightyellow",
         theme="colorblind",
         whatLabels = "std",
         style = "lisrel",
         sizeLat = 10,
         sizeLat2 = 10,
         sizeMan = 6,
         edge.color = "steelblue",
         edge.label.cex = 2,
         label.cex = 2,
         rotation = 2,
         layout = "tree2",
         intercepts = TRUE,
         residuals = FALSE,
         #residScale = 10,
         curve = 2,
         title = T,
         title.color = "black",
         cardinal = "lat cov",
         curvePivot = T,
         nCharNodes = 6,
         #nodeLabels = label,
         mar = c(2,5,2,6))
# Title 
title("Multi-group CFA on MID task Contrasts")

3 Running [semi-restricted] ESEM Model

As described in the manuscript, the restricted CFA may incorrectly account for some measurement error in the items. This may degrade the fit statistics. See Marsh et al. (2014) for an in-depth discussion.

In this case, Exploratory Structural Equation Modeling (ESEM) is used to fit a CFA pre-specified model that allows for non-zero loadings. The technique and application of ESEM is available through the psych esem and esemcomp package. Here, the esemcomp package is used to fit a model using the steps described by Mateus Silvestrin here and by Guàrdia-Olmos et al.. The github code for esemcomp is available here. Below can be used to download the esemComp package – which worked with R version 4.2.1 on x86_64-apply-dawin17.0 during September 2022.

devtools::install_github("MateusPsi/esemComp", build_vignettes = TRUE)

3.1 Selected items for ESEM

First, select the items that are consistent with those in the CFA model

# ordering so can specify numerically
esem_data = brain_set[,c("AWin_v_Neut_L_NAcc_run1"  ,"AWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_Neut_L_NAcc_run1"  ,"BWin_v_Neut_L_NAcc_run2" ,
                         "BWin_v_BLose_L_NAcc_run1" ,"BWin_v_BLose_L_NAcc_run2",
                          "AWin_v_Neut_R_NAcc_run1" , "AWin_v_Neut_R_NAcc_run2",
                          "BWin_v_Neut_R_NAcc_run1" , "BWin_v_Neut_R_NAcc_run2",
                          "BWin_v_BLose_R_NAcc_run1", "BWin_v_BLose_R_NAcc_run2",
                         # insula values apprach 
                         "AWin_v_Neut_R_Insula_run1","AWin_v_Neut_R_Insula_run2", 
                         "BWin_v_Neut_R_Insula_run1","BWin_v_Neut_R_Insula_run2", 
                         # avoidance
                         "ALose_v_Neut_L_Insula_run1","ALose_v_Neut_L_Insula_run2",
                         "BLose_v_Neut_L_Insula_run1","BLose_v_Neut_L_Insula_run2",
                         "BLose_v_BWin_L_Insula_run1","BLose_v_BWin_L_Insula_run2",
                         "ALose_v_Neut_R_Insula_run1","ALose_v_Neut_R_Insula_run2",
                         "BLose_v_Neut_R_Insula_run1","BLose_v_Neut_R_Insula_run2",
                         "BLose_v_BWin_R_Insula_run1","BLose_v_BWin_R_Insula_run2",
                         "set")]

3.2 Specify EFA Model

As described in March et al. (2014), create a target rotation for items onto factors. In this case two factors are specified by the CFA model, so factor 1 and factor 2 are specified in make_target.

# First, consistent w/ March et al. (2014), creating target rotation
# ensure they match onto variable list 
target_rot <- make_target(28,mainloadings = list(f1 = 1:16, f2 = 17:28))
esem.efa <- esem_efa(data = esem_data[,1:28], nfactors = 2,
                     target = target_rot, fm = "ml")
## Loading required namespace: GPArotation
esem.efa$loadings
## 
## Loadings:
##                            ML1    ML2   
## AWin_v_Neut_L_NAcc_run1     0.408       
## AWin_v_Neut_L_NAcc_run2     0.475       
## BWin_v_Neut_L_NAcc_run1     0.451       
## BWin_v_Neut_L_NAcc_run2     0.384       
## BWin_v_BLose_L_NAcc_run1    0.390       
## BWin_v_BLose_L_NAcc_run2    0.359       
## AWin_v_Neut_R_NAcc_run1     0.514  0.105
## AWin_v_Neut_R_NAcc_run2     0.561       
## BWin_v_Neut_R_NAcc_run1     0.412       
## BWin_v_Neut_R_NAcc_run2     0.426       
## BWin_v_BLose_R_NAcc_run1    0.449       
## BWin_v_BLose_R_NAcc_run2    0.493       
## AWin_v_Neut_R_Insula_run1   0.216       
## AWin_v_Neut_R_Insula_run2   0.253       
## BWin_v_Neut_R_Insula_run1   0.237       
## BWin_v_Neut_R_Insula_run2   0.207       
## ALose_v_Neut_L_Insula_run1         0.480
## ALose_v_Neut_L_Insula_run2         0.477
## BLose_v_Neut_L_Insula_run1         0.433
## BLose_v_Neut_L_Insula_run2         0.423
## BLose_v_BWin_L_Insula_run1         0.457
## BLose_v_BWin_L_Insula_run2         0.454
## ALose_v_Neut_R_Insula_run1         0.475
## ALose_v_Neut_R_Insula_run2         0.435
## BLose_v_Neut_R_Insula_run1         0.454
## BLose_v_Neut_R_Insula_run2         0.454
## BLose_v_BWin_R_Insula_run1         0.207
## BLose_v_BWin_R_Insula_run2         0.198
## 
##                  ML1   ML2
## SS loadings    2.625 2.196
## Proportion Var 0.094 0.078
## Cumulative Var 0.094 0.172

Using item that loads highest on factor 1 and lowest on factor 2 and vice versa, and define as anchor using find_referents

# per the example from Mateus Silverstrin, need to define anchor for each factor (value to loads highers on 1 factor and lowest on other)
anchor <- find_referents(efa_object = esem.efa,factor_names = c("f1","f2"))

Once the esem efa and anchors are defined, use syntax_composer to specied the esem model. This will produce a lavaan specified model that references starting values that will be used in the cfa model

# Pull starting parameters
esem_mid_model <- syntax_composer(efa_object = esem.efa, referents = anchor)

3.3 Run ESEM model

3.3.1 Specified Model

The starting values are printed below to provide reference for how starting values differ from a strict CFA model. Notice, how some values that were original not fit onto the Approach factor (f1), such as big lose contrasts, they are now specified with loading values that are between .05 to -.05.

cat(esem_mid_model)
## f1 =~ start(0.408)*AWin_v_Neut_L_NAcc_run1+
## start(0.475)*AWin_v_Neut_L_NAcc_run2+
## start(0.451)*BWin_v_Neut_L_NAcc_run1+
## start(0.384)*BWin_v_Neut_L_NAcc_run2+
## start(0.39)*BWin_v_BLose_L_NAcc_run1+
## start(0.359)*BWin_v_BLose_L_NAcc_run2+
## start(0.514)*AWin_v_Neut_R_NAcc_run1+
## start(0.561)*AWin_v_Neut_R_NAcc_run2+
## start(0.412)*BWin_v_Neut_R_NAcc_run1+
## start(0.426)*BWin_v_Neut_R_NAcc_run2+
## start(0.449)*BWin_v_BLose_R_NAcc_run1+
## start(0.493)*BWin_v_BLose_R_NAcc_run2+
## start(0.216)*AWin_v_Neut_R_Insula_run1+
## start(0.253)*AWin_v_Neut_R_Insula_run2+
## start(0.237)*BWin_v_Neut_R_Insula_run1+
## start(0.207)*BWin_v_Neut_R_Insula_run2+
## 0.056*ALose_v_Neut_L_Insula_run1+
## start(0.058)*ALose_v_Neut_L_Insula_run2+
## start(-0.017)*BLose_v_Neut_L_Insula_run1+
## start(-0.013)*BLose_v_Neut_L_Insula_run2+
## start(-0.006)*BLose_v_BWin_L_Insula_run1+
## start(0.031)*BLose_v_BWin_L_Insula_run2+
## start(-0.041)*ALose_v_Neut_R_Insula_run1+
## start(-0.044)*ALose_v_Neut_R_Insula_run2+
## start(-0.027)*BLose_v_Neut_R_Insula_run1+
## start(-0.019)*BLose_v_Neut_R_Insula_run2+
## start(-0.045)*BLose_v_BWin_R_Insula_run1+
## start(-0.049)*BLose_v_BWin_R_Insula_run2 
## 
## f2 =~ start(-0.052)*AWin_v_Neut_L_NAcc_run1+
## start(-0.015)*AWin_v_Neut_L_NAcc_run2+
## start(-0.013)*BWin_v_Neut_L_NAcc_run1+
## start(-0.002)*BWin_v_Neut_L_NAcc_run2+
## start(-0.099)*BWin_v_BLose_L_NAcc_run1+
## start(-0.082)*BWin_v_BLose_L_NAcc_run2+
## start(0.105)*AWin_v_Neut_R_NAcc_run1+
## 0.091*AWin_v_Neut_R_NAcc_run2+
## start(0.037)*BWin_v_Neut_R_NAcc_run1+
## start(0.008)*BWin_v_Neut_R_NAcc_run2+
## start(-0.031)*BWin_v_BLose_R_NAcc_run1+
## start(0.026)*BWin_v_BLose_R_NAcc_run2+
## start(-0.026)*AWin_v_Neut_R_Insula_run1+
## start(-0.012)*AWin_v_Neut_R_Insula_run2+
## start(-0.016)*BWin_v_Neut_R_Insula_run1+
## start(-0.077)*BWin_v_Neut_R_Insula_run2+
## start(0.48)*ALose_v_Neut_L_Insula_run1+
## start(0.477)*ALose_v_Neut_L_Insula_run2+
## start(0.433)*BLose_v_Neut_L_Insula_run1+
## start(0.423)*BLose_v_Neut_L_Insula_run2+
## start(0.457)*BLose_v_BWin_L_Insula_run1+
## start(0.454)*BLose_v_BWin_L_Insula_run2+
## start(0.475)*ALose_v_Neut_R_Insula_run1+
## start(0.435)*ALose_v_Neut_R_Insula_run2+
## start(0.454)*BLose_v_Neut_R_Insula_run1+
## start(0.454)*BLose_v_Neut_R_Insula_run2+
## start(0.207)*BLose_v_BWin_R_Insula_run1+
## start(0.198)*BLose_v_BWin_R_Insula_run2

3.3.2 Running full ESEM model

After the EFA loadings are extracted using a target rotation, starting values are now available. These are now used to specify a less restrictive CFA model

esem_mid_fit<- cfa(esem_mid_model, esem_data[,1:28], std.lv=TRUE, meanstructure = TRUE,
                   estimator = "MLR")

Pull and add fit statistics to the out dataframe and print results to see decreases in AIC/BIC

# adding values to the CFA model fit indices
out[7,2:7] <- round(data.matrix(fitmeasures(esem_mid_fit, 
                                            fit.measures = c("chisq","df","pvalue",
                                                             "rmsea", "cfi", "srmr"))), 
                    digits=3)
out[7,8] <- round(AIC(esem_mid_fit),3)
out[7,9] <- round(BIC(esem_mid_fit),3)
out[7,1] <-  c("Overall ESEM")

out <- as.data.frame(out)

out %>% 
  knitr::kable(
    col.names = c("Model", "Chi-sq", "DF", "p value", "RMSEA", "CFI", "SRMR", "AIC", "BIC"),
    caption = "Fit statistics from CFA and ESEM models",
    booktabs = TRUE
    )
Fit statistics from CFA and ESEM models
Model Chi-sq DF p value RMSEA CFI SRMR AIC BIC
AHRB CFA 499.052 323 0 0.072 0.595 0.096 -1650.715 -1433.875
MLS CFA 525.874 323 0 0.072 0.565 0.09 -1714.866 -1486.291
ABCD CFA 1700.221 323 0 0.065 0.658 0.054 -16374.249 -15971.813
Overall CFA 1992.013 323 0 0.065 0.652 0.053 -19877.767 -19458.757
Configg MG-CFA 2725.148 969 0 0.067 0.644 0.061 -19739.83 -18482.8
Metric MG-CFA 2797.802 1019 0 0.065 0.639 0.063 -19767.175 -18765.639
Overall ESEM 2116.474 323 0 0.067 0.653 0.052 -20679.389 -20112.192

4 Running EFA [Unrestricted] model

Here, a data-driven exploratory factor analysis is performed as implemented using the (https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal)[https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal] in the stats package. The same variables as in the CFA and ESEM dataset are used.

4.1 Rec. # Factors

Taking a simple scree plot approach using the nFactors package see the recommended factors for the EFA model

fa_data <- subset(esem_data[,1:28])
par(mfrow=c(1,1))
fa.parallel(fa_data) # https://cran.r-project.org/web/packages/nFactors/nFactors.pdf

## Parallel analysis suggests that the number of factors =  14  and the number of components =  9

Comparing the above with the BIC comparison of an EFA model to determine the best fitting model based on fit statistics. Factor Analysis is submitted across a range of factors, e.g., 1-5, and the BIC is extracted from the model to determine the optimal number of factors

rec_factors <- matrix(NA, ncol = 2, nrow = 20)
colnames(rec_factors) <- c("Nfactors","BIC")

for (f in 1:20) {
  test_fac <- fa(r = esem_data[,1:28],  #raw data  
            nfactors = f, 
            rotate = "promax")
  rec_factors[f,1] <- f
  rec_factors[f,2] <-test_fac$BIC
}

bic_fact = as.data.frame(rec_factors)
lowest_bic <- which.min(bic_fact$BIC)

bic_fact %>% 
  ggplot(aes(x = Nfactors, y = BIC)) +
  geom_line(colour = 'black', linetype = 'dashed') +
  geom_vline(xintercept = bic_fact$Nfactors[lowest_bic], colour = 'red')+
  theme_minimal()

Complementing the simple scree pot and BIC to avoid biasing of recommendation factors that depend on strong correlations between bilateral regions by using parallel analysis. Parallel analysis is implemented using the paran package. Converging information is used to identify the optimal factors.

paran(x = esem_data[,1:28],
      iterations = 2000, centile = 90, quietly = FALSE, 
      status = TRUE, all = TRUE, cfa = TRUE, graph = TRUE, color = TRUE, 
      col = c("black", "red", "blue"), lty = c(1, 2, 3), lwd = 1, legend = TRUE, 
      #file = "", width = 640, height = 640, grdevice = "png", 
      seed = 111)
## 
## Using eigendecomposition of correlation matrix.
## Computing: 10%  20%  30%  40%  50%  60%  70%  80%  90%  100%
## 
## 
## Results of Horn's Parallel Analysis for factor retention
## 2000 iterations, using the 90 centile estimate
## 
## -------------------------------------------------- 
## Factor      Adjusted    Unadjusted    Estimated 
##             Eigenvalue  Eigenvalue    Bias 
## -------------------------------------------------- 
## No components passed. 
## -------------------------------------------------- 
## 1           3.437425    3.779355      0.341930
## 2           0.882779    1.179309      0.296530
## 3           0.326962    0.588390      0.261427
## 4           0.280226    0.513616      0.233389
## 5           0.286416    0.494226      0.207810
## 6           0.281301    0.465349      0.184047
## 7           0.256789    0.419734      0.162945
## 8           0.251962    0.394841      0.142879
## 9           0.222816    0.345784      0.122967
## 10          0.222248    0.327018      0.104769
## 11          0.180291    0.265699      0.085408
## 12          0.179946    0.248247      0.068300
## 13          0.180402    0.231484      0.051082
## 14          0.151434    0.185454      0.034019
## 15         -0.127279   -0.11020      0.017078
## 16         -0.137681   -0.13682      0.000860
## 17         -0.124851   -0.14096     -0.01611
## 18         -0.127005   -0.15969     -0.03268
## 19         -0.124232   -0.17290     -0.04866
## 20         -0.114268   -0.17880     -0.06453
## 21         -0.121058   -0.20152     -0.08046
## 22         -0.108396   -0.20528     -0.09689
## 23         -0.115536   -0.22874     -0.11321
## 24         -0.115498   -0.24604     -0.13055
## 25         -0.102630   -0.25084     -0.14821
## 26         -0.090550   -0.25765     -0.16710
## 27         -0.087320   -0.27431     -0.18698
## 28         -0.078230   -0.28927     -0.21104
## -------------------------------------------------- 
## 
## Adjusted eigenvalues > 0 indicate dimensions to retain.
## (14 factors    retained)

4.2 Run EFA on all data

Used the (factanal)[https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/factanal] to run EFA model. Specifying the number of factors and using the promax (non-orthogonal) rotation.

MID_efa <- factanal(x = esem_data[,1:28],  #raw data  
              factors = 2, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )

4.3 Plot EFA, Dimensions

Plot the loadings across the dimensions as represented in the affective circumplex framework.

factor.plot(ic.results = MID_efa$loadings, 
            labels = colnames(fa_data), 
            cex = .6, jiggle = FALSE,
            ylim = c(-1,1), xlim = c(-1,1),
            title = "Mutldimensional Plot of FA1 v FA2 Loadings"
            )

4.4 Plot Factors Alt.

Plot factor loadings with respect to other factors.

pairs(MID_efa$loadings, col=1:ncol(fa_data), upper.panel=NULL, main="Factor loadings")
par(xpd=TRUE) 
legend('topright', bty='n', pch='o', 
       col=1:ncol(fa_data), ncol = 3,
       attr(MID_efa$loadings, 'dimnames')[[1]], 
       title="Contrasts", 
       cex = .4)

4.5 Heatmap of factor loadings

Create a heatmap of loadings onto the provided factors.

heatmaply(round(MID_efa$loadings[,1:2],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(MID_efa$loadings[,1:2]),
               labRow = rownames(MID_efa$loadings[,1:2]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2
## AWin_v_Neut_L_NAcc_run1       0.41   -0.05
## AWin_v_Neut_L_NAcc_run2       0.47   -0.02
## BWin_v_Neut_L_NAcc_run1       0.45   -0.01
## BWin_v_Neut_L_NAcc_run2       0.38    0.00
## BWin_v_BLose_L_NAcc_run1      0.39   -0.10
## BWin_v_BLose_L_NAcc_run2      0.36   -0.08
## AWin_v_Neut_R_NAcc_run1       0.52    0.11
## AWin_v_Neut_R_NAcc_run2       0.56    0.09
## BWin_v_Neut_R_NAcc_run1       0.41    0.04
## BWin_v_Neut_R_NAcc_run2       0.43    0.01
## BWin_v_BLose_R_NAcc_run1      0.45   -0.03
## BWin_v_BLose_R_NAcc_run2      0.49    0.03
## AWin_v_Neut_R_Insula_run1     0.21   -0.03
## AWin_v_Neut_R_Insula_run2     0.25   -0.01
## BWin_v_Neut_R_Insula_run1     0.24   -0.02
## BWin_v_Neut_R_Insula_run2     0.20   -0.08
## ALose_v_Neut_L_Insula_run1    0.07    0.49
## ALose_v_Neut_L_Insula_run2    0.08    0.49
## BLose_v_Neut_L_Insula_run1    0.00    0.44
## BLose_v_Neut_L_Insula_run2    0.00    0.43
## BLose_v_BWin_L_Insula_run1    0.01    0.47
## BLose_v_BWin_L_Insula_run2    0.05    0.46
## ALose_v_Neut_R_Insula_run1   -0.02    0.48
## ALose_v_Neut_R_Insula_run2   -0.03    0.44
## BLose_v_Neut_R_Insula_run1   -0.01    0.46
## BLose_v_Neut_R_Insula_run2    0.00    0.46
## BLose_v_BWin_R_Insula_run1   -0.04    0.21
## BLose_v_BWin_R_Insula_run2   -0.04    0.20

4.5.1 Run EFA on sample specific

4.5.1.1 EFA ABCD

abcd_efadata = subset(esem_data %>% filter(set==1))

abcd_efa <- factanal(x = abcd_efadata[,1:28],  #raw data  
              factors = 2, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )
heatmaply(round(abcd_efa$loadings[,1:2],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(abcd_efa$loadings[,1:2]),
               labRow = rownames(abcd_efa$loadings[,1:2]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2
## AWin_v_Neut_L_NAcc_run1       0.40   -0.06
## AWin_v_Neut_L_NAcc_run2       0.45   -0.04
## BWin_v_Neut_L_NAcc_run1       0.47   -0.04
## BWin_v_Neut_L_NAcc_run2       0.41   -0.01
## BWin_v_BLose_L_NAcc_run1      0.42   -0.07
## BWin_v_BLose_L_NAcc_run2      0.37   -0.07
## AWin_v_Neut_R_NAcc_run1       0.54    0.12
## AWin_v_Neut_R_NAcc_run2       0.61    0.14
## BWin_v_Neut_R_NAcc_run1       0.39    0.01
## BWin_v_Neut_R_NAcc_run2       0.41   -0.01
## BWin_v_BLose_R_NAcc_run1      0.44   -0.04
## BWin_v_BLose_R_NAcc_run2      0.49    0.00
## AWin_v_Neut_R_Insula_run1     0.21   -0.04
## AWin_v_Neut_R_Insula_run2     0.25   -0.03
## BWin_v_Neut_R_Insula_run1     0.23   -0.01
## BWin_v_Neut_R_Insula_run2     0.22   -0.08
## ALose_v_Neut_L_Insula_run1    0.03    0.46
## ALose_v_Neut_L_Insula_run2    0.03    0.42
## BLose_v_Neut_L_Insula_run1    0.05    0.48
## BLose_v_Neut_L_Insula_run2    0.05    0.46
## BLose_v_BWin_L_Insula_run1    0.03    0.46
## BLose_v_BWin_L_Insula_run2    0.02    0.43
## ALose_v_Neut_R_Insula_run1    0.00    0.50
## ALose_v_Neut_R_Insula_run2   -0.01    0.44
## BLose_v_Neut_R_Insula_run1    0.02    0.51
## BLose_v_Neut_R_Insula_run2    0.04    0.50
## BLose_v_BWin_R_Insula_run1   -0.06    0.18
## BLose_v_BWin_R_Insula_run2   -0.06    0.18

4.5.1.2 EFA MLS

mls_efadata = subset(esem_data %>% filter(set==2))

mls_efa <- factanal(x = mls_efadata[,1:28],  #raw data  
              factors = 2, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )
heatmaply(round(mls_efa$loadings[,1:2],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(mls_efa$loadings[,1:2]),
               labRow = rownames(mls_efa$loadings[,1:2]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2
## AWin_v_Neut_L_NAcc_run1       0.44   -0.11
## AWin_v_Neut_L_NAcc_run2       0.49    0.09
## BWin_v_Neut_L_NAcc_run1       0.36    0.27
## BWin_v_Neut_L_NAcc_run2       0.30    0.06
## BWin_v_BLose_L_NAcc_run1      0.41    0.00
## BWin_v_BLose_L_NAcc_run2      0.48    0.12
## AWin_v_Neut_R_NAcc_run1       0.47    0.12
## AWin_v_Neut_R_NAcc_run2       0.56    0.04
## BWin_v_Neut_R_NAcc_run1       0.37    0.11
## BWin_v_Neut_R_NAcc_run2       0.36    0.05
## BWin_v_BLose_R_NAcc_run1      0.44    0.02
## BWin_v_BLose_R_NAcc_run2      0.28    0.13
## AWin_v_Neut_R_Insula_run1     0.08    0.07
## AWin_v_Neut_R_Insula_run2     0.14    0.20
## BWin_v_Neut_R_Insula_run1     0.27   -0.01
## BWin_v_Neut_R_Insula_run2     0.19    0.03
## ALose_v_Neut_L_Insula_run1    0.12    0.74
## ALose_v_Neut_L_Insula_run2    0.12    0.90
## BLose_v_Neut_L_Insula_run1   -0.25    0.16
## BLose_v_Neut_L_Insula_run2   -0.25    0.22
## BLose_v_BWin_L_Insula_run1   -0.21    0.36
## BLose_v_BWin_L_Insula_run2   -0.13    0.45
## ALose_v_Neut_R_Insula_run1   -0.18    0.39
## ALose_v_Neut_R_Insula_run2   -0.30    0.27
## BLose_v_Neut_R_Insula_run1   -0.09    0.19
## BLose_v_Neut_R_Insula_run2   -0.14    0.32
## BLose_v_BWin_R_Insula_run1    0.07    0.26
## BLose_v_BWin_R_Insula_run2    0.10    0.29

4.5.1.3 EFA AHRB

ahrb_efadata = subset(esem_data %>% filter(set==3))

ahrb_efa <- factanal(x = ahrb_efadata[,1:28],  #raw data  
              factors = 2, rotation = "promax" # oblique rotation allow for non-orthogonal structure
              )
heatmaply(round(ahrb_efa$loadings[,1:2],2) %>% print(sort = T),
          scale_fill_gradient_fun = ggplot2::scale_fill_gradient2(
                 low = "blue", 
                 high = "darkred", 
                 space = "Lab",
                 midpoint = 0, 
                 limits = c(-1, 1)
               ),
               dendrogram = "none",
               xlab = "", ylab = "", 
               main = "",
               margins = c(60,100,40,20),
               grid_color = "white",
               grid_width = 0.00001,
               titleX = FALSE,
               hide_colorbar = FALSE,
               branches_lwd = 0.1,
               label_names = c("Brain:", "Feature:", "Value"),
               fontsize_row = 9, fontsize_col = 9,
               labCol = colnames(ahrb_efa$loadings[,1:2]),
               labRow = rownames(ahrb_efa$loadings[,1:2]),
               heatmap_layers = theme(axis.line=element_blank()),
          
)
##                            Factor1 Factor2
## AWin_v_Neut_L_NAcc_run1       0.61    0.22
## AWin_v_Neut_L_NAcc_run2       0.78    0.14
## BWin_v_Neut_L_NAcc_run1       0.28   -0.03
## BWin_v_Neut_L_NAcc_run2       0.18    0.00
## BWin_v_BLose_L_NAcc_run1      0.15   -0.34
## BWin_v_BLose_L_NAcc_run2      0.18   -0.24
## AWin_v_Neut_R_NAcc_run1       0.41   -0.03
## AWin_v_Neut_R_NAcc_run2       0.36   -0.10
## BWin_v_Neut_R_NAcc_run1       0.58    0.16
## BWin_v_Neut_R_NAcc_run2       0.61    0.11
## BWin_v_BLose_R_NAcc_run1      0.40   -0.09
## BWin_v_BLose_R_NAcc_run2      0.47   -0.10
## AWin_v_Neut_R_Insula_run1     0.28   -0.12
## AWin_v_Neut_R_Insula_run2     0.23   -0.18
## BWin_v_Neut_R_Insula_run1     0.18   -0.16
## BWin_v_Neut_R_Insula_run2     0.01   -0.19
## ALose_v_Neut_L_Insula_run1    0.39    0.49
## ALose_v_Neut_L_Insula_run2    0.22    0.42
## BLose_v_Neut_L_Insula_run1    0.09    0.71
## BLose_v_Neut_L_Insula_run2    0.15    0.69
## BLose_v_BWin_L_Insula_run1   -0.11    0.39
## BLose_v_BWin_L_Insula_run2    0.15    0.36
## ALose_v_Neut_R_Insula_run1   -0.10    0.33
## ALose_v_Neut_R_Insula_run2    0.10    0.50
## BLose_v_Neut_R_Insula_run1    0.00    0.44
## BLose_v_Neut_R_Insula_run2   -0.18    0.31
## BLose_v_BWin_R_Insula_run1   -0.12    0.22
## BLose_v_BWin_R_Insula_run2   -0.06    0.23

4.6 Comparing EFA models

Calculating a coefficient of factor congruence across the three sample’s EFA models. Using function fa.congruence

fa.congruence(x = list(abcd_efa, mls_efa, ahrb_efa), digits = 2) %>% 
  knitr::kable(
    col.names = c("1. ABCD F1", "2. ABCD F2", "3. MLS F1", "4. MLS F2","5. AHRB F1", "6. AHRB F2"),
    caption = "ABCD, MLS and AHRB EFA Factor Congruence",
    booktabs = TRUE
    )
ABCD, MLS and AHRB EFA Factor Congruence
1. ABCD F1 2. ABCD F2 3. MLS F1 4. MLS F2 5. AHRB F1 6. AHRB F2
Factor1 1.00 0.03 0.89 0.21 0.85 -0.07
Factor2 0.03 1.00 -0.25 0.80 0.09 0.89
Factor1 0.89 -0.25 1.00 0.07 0.78 -0.32
Factor2 0.21 0.80 0.07 1.00 0.31 0.67
Factor1 0.85 0.09 0.78 0.31 1.00 0.15
Factor2 -0.07 0.89 -0.32 0.67 0.15 1.00

5 Running Local SEM

Running CFA for the pubertal variables in the ABCD sample using the local SEM framework described in Olaru et al (2020) implemented using the sirt package

5.1 Run LSEM

Specifying the model for the ABCD data below. For now, using the CFA model. In future [real data] implementation, will apply the EFA CFA from n = 1000 ABCD sample in the held out n = 1000 ABCD sample. To pilot, simulating a [fake] pubertal variable that is 1 to 5, as is expected in the Pubertal Developmental Scale.

#first adding random PDS variable
sim_ABCD_data$PDS <- as.integer(rtnorm(n=1000, mean = 3.5, sd = 1.5, 
                                       lower = 1, upper = 5))

lsem.MID <- sirt::lsem.estimate(data = sim_ABCD_data, moderator = 'PDS', # moderator variable
                                moderator.grid = seq(1,5,1), # moderator levels, PDS 1 - 5
                                lavmodel = MID_model, # model
                                h = 2, # bandwidth parameter 
                                residualize = FALSE, # allow mean level differences 
                                meanstructure = TRUE,
                                std.lv=TRUE
                                )
## ** Fit lavaan model
## |*****|
## |-----|
## ** Parameter summary

5.2 Summary LSEM

Summarizing output of the lsem.estimate

summary(lsem.MID)
## -----------------------------------------------------------------
## Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## R version 4.2.1 (2022-06-23) x86_64, darwin17.0 | nodename=Michaels-MacBook-Pro.local | login=root 
## 
## Function 'sirt::lsem.estimate', type='LSEM' 
## 
## 
## Call:
## sirt::lsem.estimate(data = sim_ABCD_data, moderator = "PDS", 
##     moderator.grid = seq(1, 5, 1), lavmodel = MID_model, h = 2, 
##     residualize = FALSE, meanstructure = TRUE, std.lv = TRUE)
## 
## Date of Analysis: 2022-10-29 13:17:00 
## Time difference of 6.247428 secs
## Computation Time: 6.247428 
## 
## Number of observations in datasets = 1000 
## Used observations in analysis = 1000 
## Used sampling weights: FALSE 
## Bandwidth factor = 2 
## Bandwidth = 0.507 
## Number of focal points for moderator = 5 
## 
## Used joint estimation: FALSE 
## Used sufficient statistics: FALSE 
## Used local linear smoothing: FALSE 
## Used pseudo weights: FALSE 
## Used lavaan package: TRUE 
## Used lavaan.survey package: FALSE 
## 
## Mean structure modelled: TRUE 
## 
## lavaan Model
## 
## 
## # Factor loadings
## Approach =~ AWin_v_Neut_L_NAcc_run1  + AWin_v_Neut_R_NAcc_run1  + AWin_v_Neut_R_Insula_run1 +
##             BWin_v_Neut_L_NAcc_run1  + BWin_v_Neut_R_NAcc_run1  + BWin_v_Neut_R_Insula_run1 +
##             BWin_v_BLose_L_NAcc_run1 + BWin_v_BLose_R_NAcc_run1 +
##             AWin_v_Neut_L_NAcc_run2  + AWin_v_Neut_R_NAcc_run2 + AWin_v_Neut_R_Insula_run2 +
##             BWin_v_Neut_L_NAcc_run2  + BWin_v_Neut_R_NAcc_run2  + BWin_v_Neut_R_Insula_run2 +
##             BWin_v_BLose_L_NAcc_run2 + BWin_v_BLose_R_NAcc_run2 
##                 
## Avoid =~    ALose_v_Neut_L_Insula_run1 + ALose_v_Neut_L_Insula_run1 +
##             BLose_v_Neut_L_Insula_run1 + BLose_v_Neut_R_Insula_run1 +
##             BLose_v_BWin_L_Insula_run1 + BLose_v_BWin_R_Insula_run1 +
##             ALose_v_Neut_L_Insula_run2 + ALose_v_Neut_R_Insula_run2 +
##             BLose_v_Neut_L_Insula_run2 + BLose_v_Neut_R_Insula_run2 +
##             BLose_v_BWin_L_Insula_run2 + BLose_v_BWin_R_Insula_run2 
## 
## 
## Parameter Estimate Summary
## 
##                                                       par parindex      M    SD
## 1                       Approach=~AWin_v_Neut_L_NAcc_run1        1  0.083 0.016
## 2                       Approach=~AWin_v_Neut_R_NAcc_run1        2  0.086 0.010
## 3                     Approach=~AWin_v_Neut_R_Insula_run1        3  0.042 0.007
## 4                       Approach=~BWin_v_Neut_L_NAcc_run1        4  0.092 0.009
## 5                       Approach=~BWin_v_Neut_R_NAcc_run1        5  0.070 0.013
## 6                     Approach=~BWin_v_Neut_R_Insula_run1        6  0.042 0.009
## 7                      Approach=~BWin_v_BLose_L_NAcc_run1        7  0.090 0.010
## 8                      Approach=~BWin_v_BLose_R_NAcc_run1        8  0.089 0.009
## 9                       Approach=~AWin_v_Neut_L_NAcc_run2        9  0.089 0.011
## 10                      Approach=~AWin_v_Neut_R_NAcc_run2       10  0.096 0.013
## 11                    Approach=~AWin_v_Neut_R_Insula_run2       11  0.048 0.005
## 12                      Approach=~BWin_v_Neut_L_NAcc_run2       12  0.080 0.006
## 13                      Approach=~BWin_v_Neut_R_NAcc_run2       13  0.078 0.006
## 14                    Approach=~BWin_v_Neut_R_Insula_run2       14  0.048 0.011
## 15                     Approach=~BWin_v_BLose_L_NAcc_run2       15  0.077 0.005
## 16                     Approach=~BWin_v_BLose_R_NAcc_run2       16  0.092 0.014
## 17                      Avoid=~ALose_v_Neut_L_Insula_run1       17  0.088 0.010
## 18                      Avoid=~BLose_v_Neut_L_Insula_run1       18  0.086 0.009
## 19                      Avoid=~BLose_v_Neut_R_Insula_run1       19  0.097 0.010
## 20                      Avoid=~BLose_v_BWin_L_Insula_run1       20  0.086 0.010
## 21                      Avoid=~BLose_v_BWin_R_Insula_run1       21  0.044 0.006
## 22                      Avoid=~ALose_v_Neut_L_Insula_run2       22  0.077 0.008
## 23                      Avoid=~ALose_v_Neut_R_Insula_run2       23  0.075 0.008
## 24                      Avoid=~BLose_v_Neut_L_Insula_run2       24  0.082 0.009
## 25                      Avoid=~BLose_v_Neut_R_Insula_run2       25  0.095 0.005
## 26                      Avoid=~BLose_v_BWin_L_Insula_run2       26  0.080 0.006
## 27                      Avoid=~BLose_v_BWin_R_Insula_run2       27  0.041 0.006
## 28       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       28  0.028 0.000
## 29       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       29  0.031 0.004
## 30   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       30  0.029 0.001
## 31       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       31  0.025 0.002
## 32       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       32  0.029 0.001
## 33   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       33  0.031 0.002
## 34     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       34  0.029 0.002
## 35     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       35  0.029 0.001
## 36       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       36  0.027 0.001
## 37       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       37  0.028 0.001
## 38   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       38  0.028 0.002
## 39       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       39  0.030 0.002
## 40       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       40  0.030 0.002
## 41   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       41  0.031 0.002
## 42     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       42  0.028 0.001
## 43     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       43  0.028 0.001
## 44 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       44  0.029 0.002
## 45 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       45  0.028 0.002
## 46 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       46  0.025 0.003
## 47 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       47  0.030 0.001
## 48 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       48  0.030 0.001
## 49 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       49  0.029 0.002
## 50 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       50  0.032 0.002
## 51 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51  0.030 0.002
## 52 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52  0.028 0.001
## 53 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       53  0.029 0.002
## 54 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       54  0.029 0.000
## 55                                     Approach~~Approach       55  1.000 0.000
## 56                                           Avoid~~Avoid       56  1.000 0.000
## 57                                        Approach~~Avoid       57 -0.564 0.043
## 58                              AWin_v_Neut_L_NAcc_run1~1       58 -0.003 0.008
## 59                              AWin_v_Neut_R_NAcc_run1~1       59 -0.005 0.007
## 60                            AWin_v_Neut_R_Insula_run1~1       60  0.008 0.003
## 61                              BWin_v_Neut_L_NAcc_run1~1       61 -0.010 0.012
## 62                              BWin_v_Neut_R_NAcc_run1~1       62 -0.005 0.006
## 63                            BWin_v_Neut_R_Insula_run1~1       63  0.013 0.005
## 64                             BWin_v_BLose_L_NAcc_run1~1       64 -0.001 0.008
## 65                             BWin_v_BLose_R_NAcc_run1~1       65 -0.003 0.003
## 66                              AWin_v_Neut_L_NAcc_run2~1       66 -0.004 0.008
## 67                              AWin_v_Neut_R_NAcc_run2~1       67  0.002 0.009
## 68                            AWin_v_Neut_R_Insula_run2~1       68  0.006 0.006
## 69                              BWin_v_Neut_L_NAcc_run2~1       69 -0.004 0.011
## 70                              BWin_v_Neut_R_NAcc_run2~1       70  0.000 0.009
## 71                            BWin_v_Neut_R_Insula_run2~1       71 -0.001 0.001
## 72                             BWin_v_BLose_L_NAcc_run2~1       72 -0.007 0.007
## 73                             BWin_v_BLose_R_NAcc_run2~1       73 -0.006 0.006
## 74                           ALose_v_Neut_L_Insula_run1~1       74 -0.004 0.006
## 75                           BLose_v_Neut_L_Insula_run1~1       75  0.004 0.001
## 76                           BLose_v_Neut_R_Insula_run1~1       76  0.015 0.006
## 77                           BLose_v_BWin_L_Insula_run1~1       77  0.008 0.010
## 78                           BLose_v_BWin_R_Insula_run1~1       78  0.003 0.010
## 79                           ALose_v_Neut_L_Insula_run2~1       79 -0.001 0.001
## 80                           ALose_v_Neut_R_Insula_run2~1       80  0.001 0.008
## 81                           BLose_v_Neut_L_Insula_run2~1       81  0.011 0.009
## 82                           BLose_v_Neut_R_Insula_run2~1       82  0.005 0.007
## 83                           BLose_v_BWin_L_Insula_run2~1       83  0.005 0.007
## 84                           BLose_v_BWin_R_Insula_run2~1       84 -0.004 0.012
## 85                                             Approach~1       85  0.000 0.000
## 86                                                Avoid~1       86  0.000 0.000
## 87                                                  rmsea       87  0.078 0.006
## 88                                                    cfi       88  0.578 0.042
## 89                                                    tli       89  0.541 0.046
## 90                                                    gfi       90  0.857 0.015
## 91                                                   srmr       91  0.063 0.004
##      MAD    Min    Max lin_int lin_slo SD_nonlin
## 1  0.014  0.065  0.106   0.043   0.015     0.005
## 2  0.007  0.080  0.110   0.104  -0.007     0.007
## 3  0.006  0.035  0.051   0.042   0.000     0.007
## 4  0.008  0.084  0.108   0.083   0.004     0.008
## 5  0.011  0.047  0.092   0.043   0.010     0.009
## 6  0.008  0.030  0.057   0.041   0.001     0.009
## 7  0.009  0.076  0.101   0.069   0.008     0.006
## 8  0.009  0.081  0.104   0.081   0.003     0.009
## 9  0.010  0.075  0.105   0.062   0.010     0.005
## 10 0.012  0.079  0.113   0.084   0.004     0.013
## 11 0.004  0.043  0.055   0.052  -0.002     0.004
## 12 0.005  0.073  0.088   0.076   0.002     0.006
## 13 0.006  0.069  0.089   0.067   0.004     0.005
## 14 0.011  0.038  0.066   0.043   0.002     0.011
## 15 0.005  0.071  0.086   0.075   0.001     0.005
## 16 0.013  0.065  0.106   0.060   0.012     0.008
## 17 0.009  0.080  0.100   0.110  -0.008     0.005
## 18 0.008  0.072  0.096   0.075   0.004     0.009
## 19 0.010  0.079  0.105   0.106  -0.003     0.009
## 20 0.009  0.075  0.104   0.091  -0.002     0.010
## 21 0.006  0.035  0.049   0.033   0.004     0.004
## 22 0.007  0.066  0.089   0.089  -0.005     0.006
## 23 0.006  0.070  0.095   0.090  -0.006     0.006
## 24 0.008  0.067  0.091   0.074   0.003     0.009
## 25 0.004  0.089  0.102   0.100  -0.002     0.005
## 26 0.004  0.074  0.094   0.094  -0.005     0.003
## 27 0.006  0.034  0.048   0.030   0.004     0.005
## 28 0.000  0.027  0.028   0.027   0.000     0.000
## 29 0.003  0.024  0.036   0.022   0.003     0.001
## 30 0.001  0.027  0.030   0.028   0.001     0.001
## 31 0.002  0.023  0.028   0.028  -0.001     0.002
## 32 0.001  0.027  0.030   0.029   0.000     0.001
## 33 0.002  0.025  0.032   0.026   0.002     0.002
## 34 0.002  0.025  0.032   0.028   0.000     0.002
## 35 0.001  0.026  0.030   0.027   0.001     0.001
## 36 0.001  0.026  0.029   0.028  -0.001     0.001
## 37 0.001  0.027  0.030   0.028   0.000     0.001
## 38 0.002  0.027  0.032   0.024   0.001     0.001
## 39 0.001  0.025  0.032   0.026   0.001     0.001
## 40 0.002  0.028  0.031   0.031   0.000     0.002
## 41 0.002  0.025  0.033   0.027   0.001     0.002
## 42 0.001  0.026  0.029   0.027   0.000     0.001
## 43 0.001  0.027  0.031   0.026   0.001     0.001
## 44 0.002  0.026  0.032   0.028   0.000     0.002
## 45 0.001  0.025  0.031   0.028   0.000     0.002
## 46 0.002  0.021  0.028   0.020   0.002     0.002
## 47 0.001  0.029  0.031   0.029   0.000     0.001
## 48 0.001  0.029  0.031   0.032   0.000     0.001
## 49 0.001  0.026  0.032   0.029   0.000     0.002
## 50 0.001  0.029  0.034   0.036  -0.001     0.001
## 51 0.002  0.028  0.034   0.033  -0.001     0.002
## 52 0.000  0.027  0.029   0.028   0.000     0.001
## 53 0.002  0.027  0.032   0.035  -0.002     0.001
## 54 0.000  0.028  0.030   0.030   0.000     0.000
## 55 0.000  1.000  1.000   1.000   0.000     0.000
## 56 0.000  1.000  1.000   1.000   0.000     0.000
## 57 0.029 -0.597 -0.462  -0.486  -0.029     0.031
## 58 0.007 -0.012  0.010   0.003  -0.002     0.007
## 59 0.005 -0.023 -0.001  -0.016   0.004     0.006
## 60 0.002  0.004  0.012   0.004   0.001     0.003
## 61 0.011 -0.026  0.004  -0.034   0.009     0.008
## 62 0.005 -0.016  0.003   0.000  -0.002     0.006
## 63 0.004  0.006  0.020   0.004   0.003     0.003
## 64 0.007 -0.019  0.006   0.017  -0.007     0.005
## 65 0.002 -0.007  0.004  -0.001  -0.001     0.003
## 66 0.007 -0.016  0.008  -0.001  -0.001     0.008
## 67 0.007 -0.019  0.010  -0.017   0.007     0.006
## 68 0.005 -0.002  0.013   0.004   0.001     0.006
## 69 0.010 -0.016  0.011  -0.021   0.007     0.009
## 70 0.007 -0.010  0.011  -0.014   0.005     0.007
## 71 0.001 -0.003  0.000  -0.003   0.001     0.000
## 72 0.006 -0.020  0.001   0.001  -0.003     0.006
## 73 0.005 -0.017  0.003   0.006  -0.004     0.003
## 74 0.005 -0.009  0.005   0.005  -0.003     0.005
## 75 0.001  0.003  0.006   0.003   0.000     0.001
## 76 0.005  0.006  0.025   0.017   0.000     0.006
## 77 0.009 -0.008  0.021   0.007   0.000     0.010
## 78 0.009 -0.005  0.019   0.016  -0.005     0.009
## 79 0.001 -0.002  0.001   0.001  -0.001     0.001
## 80 0.007 -0.005  0.018  -0.015   0.006     0.005
## 81 0.007 -0.002  0.027  -0.010   0.008     0.003
## 82 0.007 -0.003  0.014  -0.001   0.002     0.006
## 83 0.007 -0.003  0.017   0.008  -0.001     0.007
## 84 0.011 -0.014  0.019   0.026  -0.011     0.005
## 85 0.000  0.000  0.000   0.000   0.000     0.000
## 86 0.000  0.000  0.000   0.000   0.000     0.000
## 87 0.004  0.073  0.090   0.089  -0.004     0.004
## 88 0.040  0.528  0.627   0.473   0.039     0.016
## 89 0.044  0.488  0.594   0.428   0.042     0.017
## 90 0.011  0.824  0.871   0.827   0.011     0.010
## 91 0.003  0.061  0.072   0.073  -0.003     0.002
## 
## Distribution of Moderator: Density and Effective Sample Size
## 
## M=2.702 | SD=1.009
## 
##   moderator   wgt    Neff
## 1         1 0.141 180.999
## 2         2 0.279 344.553
## 3         3 0.317 394.505
## 4         4 0.263 308.413
## 5         5 0.000  37.712
## 
##    variable       M      SD    min     max
## 1 moderator   2.702   1.009  1.000   4.000
## 2       wgt   0.200   0.130  0.000   0.317
## 3      Neff 253.236 144.056 37.712 394.505

5.3 Plot LSEM

Plotting the lsem.estimate for the first 20 indexes.

plot(lsem.MID, parindex=1:20)

5.4 Permutation Test LSEM

Running permutation test of LSEM model. In this case, using 10 permutation to save on time. In future iterations, permutations will be 1000.

lsem.permuted <- sirt::lsem.permutationTest(lsem.object = lsem.MID,
                                            B = 10, # permutations 
                                            residualize = FALSE) 
## Permutation test LSEM 
## 1  2  3  4  5  6  7  8  9  10
summary(lsem.permuted) # examine results
## -----------------------------------------------------------------
## Permutation Test for Local Structural Equation Model 
## 
## sirt 3.12-66 (2022-05-16 12:27:54) 
## lavaan 0.6-12 (2022-07-04 16:40:02 UTC) 
## 
## Function 'sirt::lsem.permutationTest' 
## 
## 
## Call:
## sirt::lsem.permutationTest(lsem.object = lsem.MID, B = 10, residualize = FALSE)
## 
## Date of Analysis: 2022-10-29 13:18:00 
## Time difference of 58.0105 secs
## Computation Time: 58.0105 
## 
## Number of permutations = 10 
## Percentage of non-converged datasets = 0 
## Number of observations=1000 
## Bandwidth factor=2 
## Bandwidth=0.507 
## Number of focal points for moderator=5 
## 
## lavaan Model
## 
## 
## # Factor loadings
## Approach =~ AWin_v_Neut_L_NAcc_run1  + AWin_v_Neut_R_NAcc_run1  + AWin_v_Neut_R_Insula_run1 +
##             BWin_v_Neut_L_NAcc_run1  + BWin_v_Neut_R_NAcc_run1  + BWin_v_Neut_R_Insula_run1 +
##             BWin_v_BLose_L_NAcc_run1 + BWin_v_BLose_R_NAcc_run1 +
##             AWin_v_Neut_L_NAcc_run2  + AWin_v_Neut_R_NAcc_run2 + AWin_v_Neut_R_Insula_run2 +
##             BWin_v_Neut_L_NAcc_run2  + BWin_v_Neut_R_NAcc_run2  + BWin_v_Neut_R_Insula_run2 +
##             BWin_v_BLose_L_NAcc_run2 + BWin_v_BLose_R_NAcc_run2 
##                 
## Avoid =~    ALose_v_Neut_L_Insula_run1 + ALose_v_Neut_L_Insula_run1 +
##             BLose_v_Neut_L_Insula_run1 + BLose_v_Neut_R_Insula_run1 +
##             BLose_v_BWin_L_Insula_run1 + BLose_v_BWin_R_Insula_run1 +
##             ALose_v_Neut_L_Insula_run2 + ALose_v_Neut_R_Insula_run2 +
##             BLose_v_Neut_L_Insula_run2 + BLose_v_Neut_R_Insula_run2 +
##             BLose_v_BWin_L_Insula_run2 + BLose_v_BWin_R_Insula_run2 
## 
## 
## Global Test Statistics
## 
##                                                       par      M    SD SD_p
## 1                       Approach=~AWin_v_Neut_L_NAcc_run1  0.083 0.016  0.1
## 2                       Approach=~AWin_v_Neut_R_NAcc_run1  0.086 0.010  0.5
## 3                     Approach=~AWin_v_Neut_R_Insula_run1  0.042 0.007  0.4
## 4                       Approach=~BWin_v_Neut_L_NAcc_run1  0.092 0.009  0.2
## 5                       Approach=~BWin_v_Neut_R_NAcc_run1  0.070 0.013  0.1
## 6                     Approach=~BWin_v_Neut_R_Insula_run1  0.042 0.009  0.5
## 7                      Approach=~BWin_v_BLose_L_NAcc_run1  0.090 0.010  0.1
## 8                      Approach=~BWin_v_BLose_R_NAcc_run1  0.089 0.009  0.3
## 9                       Approach=~AWin_v_Neut_L_NAcc_run2  0.089 0.011  0.3
## 10                      Approach=~AWin_v_Neut_R_NAcc_run2  0.096 0.013  0.0
## 11                    Approach=~AWin_v_Neut_R_Insula_run2  0.048 0.005  0.9
## 12                      Approach=~BWin_v_Neut_L_NAcc_run2  0.080 0.006  0.6
## 13                      Approach=~BWin_v_Neut_R_NAcc_run2  0.078 0.006  0.4
## 14                    Approach=~BWin_v_Neut_R_Insula_run2  0.048 0.011  0.2
## 15                     Approach=~BWin_v_BLose_L_NAcc_run2  0.077 0.005  0.7
## 16                     Approach=~BWin_v_BLose_R_NAcc_run2  0.092 0.014  0.2
## 17                      Avoid=~ALose_v_Neut_L_Insula_run1  0.088 0.010  0.5
## 18                      Avoid=~BLose_v_Neut_L_Insula_run1  0.086 0.009  0.5
## 19                      Avoid=~BLose_v_Neut_R_Insula_run1  0.097 0.010  0.4
## 20                      Avoid=~BLose_v_BWin_L_Insula_run1  0.086 0.010  0.3
## 21                      Avoid=~BLose_v_BWin_R_Insula_run1  0.044 0.006  0.6
## 22                      Avoid=~ALose_v_Neut_L_Insula_run2  0.077 0.008  0.5
## 23                      Avoid=~ALose_v_Neut_R_Insula_run2  0.075 0.008  0.3
## 24                      Avoid=~BLose_v_Neut_L_Insula_run2  0.082 0.009  0.4
## 25                      Avoid=~BLose_v_Neut_R_Insula_run2  0.095 0.005  1.0
## 26                      Avoid=~BLose_v_BWin_L_Insula_run2  0.080 0.006  0.9
## 27                      Avoid=~BLose_v_BWin_R_Insula_run2  0.041 0.006  0.9
## 28       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1  0.028 0.000  1.0
## 29       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1  0.031 0.004  0.2
## 30   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1  0.029 0.001  0.6
## 31       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1  0.025 0.002  0.1
## 32       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1  0.029 0.001  0.9
## 33   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1  0.031 0.002  0.3
## 34     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1  0.029 0.002  0.1
## 35     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1  0.029 0.001  0.6
## 36       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2  0.027 0.001  0.8
## 37       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2  0.028 0.001  0.9
## 38   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2  0.028 0.002  0.3
## 39       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2  0.030 0.002  0.3
## 40       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2  0.030 0.002  0.5
## 41   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2  0.031 0.002  0.2
## 42     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2  0.028 0.001  0.9
## 43     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2  0.028 0.001  0.5
## 44 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1  0.029 0.002  0.2
## 45 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1  0.028 0.002  0.4
## 46 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1  0.025 0.003  0.1
## 47 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1  0.030 0.001  1.0
## 48 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1  0.030 0.001  0.9
## 49 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2  0.029 0.002  0.6
## 50 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2  0.032 0.002  0.4
## 51 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2  0.030 0.002  0.3
## 52 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2  0.028 0.001  0.9
## 53 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2  0.029 0.002  0.4
## 54 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2  0.029 0.000  1.0
## 55                                     Approach~~Approach  1.000 0.000  1.0
## 56                                           Avoid~~Avoid  1.000 0.000  1.0
## 57                                        Approach~~Avoid -0.564 0.043  0.3
## 58                              AWin_v_Neut_L_NAcc_run1~1 -0.003 0.008  0.2
## 59                              AWin_v_Neut_R_NAcc_run1~1 -0.005 0.007  0.3
## 60                            AWin_v_Neut_R_Insula_run1~1  0.008 0.003  0.8
## 61                              BWin_v_Neut_L_NAcc_run1~1 -0.010 0.012  0.0
## 62                              BWin_v_Neut_R_NAcc_run1~1 -0.005 0.006  0.9
## 63                            BWin_v_Neut_R_Insula_run1~1  0.013 0.005  0.5
## 64                             BWin_v_BLose_L_NAcc_run1~1 -0.001 0.008  0.1
## 65                             BWin_v_BLose_R_NAcc_run1~1 -0.003 0.003  0.9
## 66                              AWin_v_Neut_L_NAcc_run2~1 -0.004 0.008  0.4
## 67                              AWin_v_Neut_R_NAcc_run2~1  0.002 0.009  0.2
## 68                            AWin_v_Neut_R_Insula_run2~1  0.006 0.006  0.7
## 69                              BWin_v_Neut_L_NAcc_run2~1 -0.004 0.011  0.1
## 70                              BWin_v_Neut_R_NAcc_run2~1  0.000 0.009  0.3
## 71                            BWin_v_Neut_R_Insula_run2~1 -0.001 0.001  1.0
## 72                             BWin_v_BLose_L_NAcc_run2~1 -0.007 0.007  0.4
## 73                             BWin_v_BLose_R_NAcc_run2~1 -0.006 0.006  0.5
## 74                           ALose_v_Neut_L_Insula_run1~1 -0.004 0.006  0.7
## 75                           BLose_v_Neut_L_Insula_run1~1  0.004 0.001  1.0
## 76                           BLose_v_Neut_R_Insula_run1~1  0.015 0.006  0.5
## 77                           BLose_v_BWin_L_Insula_run1~1  0.008 0.010  0.0
## 78                           BLose_v_BWin_R_Insula_run1~1  0.003 0.010  0.2
## 79                           ALose_v_Neut_L_Insula_run2~1 -0.001 0.001  1.0
## 80                           ALose_v_Neut_R_Insula_run2~1  0.001 0.008  0.4
## 81                           BLose_v_Neut_L_Insula_run2~1  0.011 0.009  0.2
## 82                           BLose_v_Neut_R_Insula_run2~1  0.005 0.007  0.4
## 83                           BLose_v_BWin_L_Insula_run2~1  0.005 0.007  0.3
## 84                           BLose_v_BWin_R_Insula_run2~1 -0.004 0.012  0.1
## 85                                             Approach~1  0.000 0.000  1.0
## 86                                                Avoid~1  0.000 0.000  1.0
## 87                                                  rmsea  0.078 0.006  0.1
## 88                                                    cfi  0.578 0.042  0.4
## 89                                                    tli  0.541 0.046  0.4
## 90                                                    gfi  0.857 0.015  0.2
## 91                                                   srmr  0.063 0.004  0.4
##      MAD MAD_p lin_slo lin_slo_p
## 1  0.014   0.0   0.015       0.0
## 2  0.007   0.7  -0.007       0.4
## 3  0.006   0.5   0.000       0.8
## 4  0.008   0.1   0.004       0.6
## 5  0.011   0.0   0.010       0.0
## 6  0.008   0.4   0.001       0.8
## 7  0.009   0.1   0.008       0.4
## 8  0.009   0.2   0.003       0.6
## 9  0.010   0.3   0.010       0.2
## 10 0.012   0.0   0.004       0.2
## 11 0.004   0.8  -0.002       1.0
## 12 0.005   0.5   0.002       0.6
## 13 0.006   0.4   0.004       0.4
## 14 0.011   0.1   0.002       1.0
## 15 0.005   0.7   0.001       0.4
## 16 0.013   0.2   0.012       0.2
## 17 0.009   0.5  -0.008       0.8
## 18 0.008   0.5   0.004       0.4
## 19 0.010   0.3  -0.003       0.4
## 20 0.009   0.2  -0.002       0.4
## 21 0.006   0.5   0.004       0.6
## 22 0.007   0.5  -0.005       0.4
## 23 0.006   0.4  -0.006       0.4
## 24 0.008   0.3   0.003       0.4
## 25 0.004   1.0  -0.002       0.6
## 26 0.004   0.9  -0.005       0.4
## 27 0.006   0.9   0.004       0.6
## 28 0.000   1.0   0.000       0.2
## 29 0.003   0.2   0.003       0.2
## 30 0.001   0.9   0.001       0.6
## 31 0.002   0.1  -0.001       0.2
## 32 0.001   0.8   0.000       0.4
## 33 0.002   0.4   0.002       0.2
## 34 0.002   0.1   0.000       0.6
## 35 0.001   0.7   0.001       0.6
## 36 0.001   0.7  -0.001       0.8
## 37 0.001   0.9   0.000       0.4
## 38 0.002   0.0   0.001       0.2
## 39 0.001   0.4   0.001       0.4
## 40 0.002   0.5   0.000       0.8
## 41 0.002   0.3   0.001       0.4
## 42 0.001   0.9   0.000       0.4
## 43 0.001   0.5   0.001       0.2
## 44 0.002   0.1   0.000       0.6
## 45 0.001   0.5   0.000       1.0
## 46 0.002   0.2   0.002       0.0
## 47 0.001   0.9   0.000       0.6
## 48 0.001   0.9   0.000       0.6
## 49 0.001   0.6   0.000       0.4
## 50 0.001   0.4  -0.001       0.2
## 51 0.002   0.4  -0.001       0.0
## 52 0.000   0.9   0.000       1.0
## 53 0.002   0.0  -0.002       0.4
## 54 0.000   1.0   0.000       1.0
## 55 0.000   1.0   0.000       1.0
## 56 0.000   1.0   0.000       1.0
## 57 0.029   0.4  -0.029       0.2
## 58 0.007   0.2  -0.002       0.4
## 59 0.005   0.7   0.004       0.8
## 60 0.002   0.8   0.001       0.6
## 61 0.011   0.0   0.009       0.0
## 62 0.005   0.7  -0.002       0.2
## 63 0.004   0.6   0.003       0.8
## 64 0.007   0.1  -0.007       0.0
## 65 0.002   0.9  -0.001       0.6
## 66 0.007   0.3  -0.001       0.8
## 67 0.007   0.3   0.007       0.2
## 68 0.005   0.7   0.001       0.6
## 69 0.010   0.2   0.007       0.4
## 70 0.007   0.4   0.005       0.2
## 71 0.001   1.0   0.001       0.4
## 72 0.006   0.3  -0.003       0.4
## 73 0.005   0.6  -0.004       0.2
## 74 0.005   0.8  -0.003       0.4
## 75 0.001   1.0   0.000       0.4
## 76 0.005   0.5   0.000       0.6
## 77 0.009   0.1   0.000       0.4
## 78 0.009   0.1  -0.005       0.2
## 79 0.001   1.0  -0.001       1.0
## 80 0.007   0.4   0.006       0.2
## 81 0.007   0.4   0.008       0.0
## 82 0.007   0.3   0.002       0.6
## 83 0.007   0.2  -0.001       1.0
## 84 0.011   0.1  -0.011       0.0
## 85 0.000   1.0   0.000       1.0
## 86 0.000   1.0   0.000       1.0
## 87 0.004   0.2  -0.004       0.2
## 88 0.040   0.2   0.039       0.4
## 89 0.044   0.2   0.042       0.4
## 90 0.011   0.2   0.011       0.0
## 91 0.003   0.1  -0.003       0.4
## 
## Pointwise Test Statistics
## 
##                                                        par parindex moderator
## 1                        Approach=~AWin_v_Neut_L_NAcc_run1        1         1
## 2                        Approach=~AWin_v_Neut_L_NAcc_run1        1         2
## 3                        Approach=~AWin_v_Neut_L_NAcc_run1        1         3
## 4                        Approach=~AWin_v_Neut_L_NAcc_run1        1         4
## 5                        Approach=~AWin_v_Neut_L_NAcc_run1        1         5
## 6                        Approach=~AWin_v_Neut_R_NAcc_run1        2         1
## 7                        Approach=~AWin_v_Neut_R_NAcc_run1        2         2
## 8                        Approach=~AWin_v_Neut_R_NAcc_run1        2         3
## 9                        Approach=~AWin_v_Neut_R_NAcc_run1        2         4
## 10                       Approach=~AWin_v_Neut_R_NAcc_run1        2         5
## 11                     Approach=~AWin_v_Neut_R_Insula_run1        3         1
## 12                     Approach=~AWin_v_Neut_R_Insula_run1        3         2
## 13                     Approach=~AWin_v_Neut_R_Insula_run1        3         3
## 14                     Approach=~AWin_v_Neut_R_Insula_run1        3         4
## 15                     Approach=~AWin_v_Neut_R_Insula_run1        3         5
## 16                       Approach=~BWin_v_Neut_L_NAcc_run1        4         1
## 17                       Approach=~BWin_v_Neut_L_NAcc_run1        4         2
## 18                       Approach=~BWin_v_Neut_L_NAcc_run1        4         3
## 19                       Approach=~BWin_v_Neut_L_NAcc_run1        4         4
## 20                       Approach=~BWin_v_Neut_L_NAcc_run1        4         5
## 21                       Approach=~BWin_v_Neut_R_NAcc_run1        5         1
## 22                       Approach=~BWin_v_Neut_R_NAcc_run1        5         2
## 23                       Approach=~BWin_v_Neut_R_NAcc_run1        5         3
## 24                       Approach=~BWin_v_Neut_R_NAcc_run1        5         4
## 25                       Approach=~BWin_v_Neut_R_NAcc_run1        5         5
## 26                     Approach=~BWin_v_Neut_R_Insula_run1        6         1
## 27                     Approach=~BWin_v_Neut_R_Insula_run1        6         2
## 28                     Approach=~BWin_v_Neut_R_Insula_run1        6         3
## 29                     Approach=~BWin_v_Neut_R_Insula_run1        6         4
## 30                     Approach=~BWin_v_Neut_R_Insula_run1        6         5
## 31                      Approach=~BWin_v_BLose_L_NAcc_run1        7         1
## 32                      Approach=~BWin_v_BLose_L_NAcc_run1        7         2
## 33                      Approach=~BWin_v_BLose_L_NAcc_run1        7         3
## 34                      Approach=~BWin_v_BLose_L_NAcc_run1        7         4
## 35                      Approach=~BWin_v_BLose_L_NAcc_run1        7         5
## 36                      Approach=~BWin_v_BLose_R_NAcc_run1        8         1
## 37                      Approach=~BWin_v_BLose_R_NAcc_run1        8         2
## 38                      Approach=~BWin_v_BLose_R_NAcc_run1        8         3
## 39                      Approach=~BWin_v_BLose_R_NAcc_run1        8         4
## 40                      Approach=~BWin_v_BLose_R_NAcc_run1        8         5
## 41                       Approach=~AWin_v_Neut_L_NAcc_run2        9         1
## 42                       Approach=~AWin_v_Neut_L_NAcc_run2        9         2
## 43                       Approach=~AWin_v_Neut_L_NAcc_run2        9         3
## 44                       Approach=~AWin_v_Neut_L_NAcc_run2        9         4
## 45                       Approach=~AWin_v_Neut_L_NAcc_run2        9         5
## 46                       Approach=~AWin_v_Neut_R_NAcc_run2       10         1
## 47                       Approach=~AWin_v_Neut_R_NAcc_run2       10         2
## 48                       Approach=~AWin_v_Neut_R_NAcc_run2       10         3
## 49                       Approach=~AWin_v_Neut_R_NAcc_run2       10         4
## 50                       Approach=~AWin_v_Neut_R_NAcc_run2       10         5
## 51                     Approach=~AWin_v_Neut_R_Insula_run2       11         1
## 52                     Approach=~AWin_v_Neut_R_Insula_run2       11         2
## 53                     Approach=~AWin_v_Neut_R_Insula_run2       11         3
## 54                     Approach=~AWin_v_Neut_R_Insula_run2       11         4
## 55                     Approach=~AWin_v_Neut_R_Insula_run2       11         5
## 56                       Approach=~BWin_v_Neut_L_NAcc_run2       12         1
## 57                       Approach=~BWin_v_Neut_L_NAcc_run2       12         2
## 58                       Approach=~BWin_v_Neut_L_NAcc_run2       12         3
## 59                       Approach=~BWin_v_Neut_L_NAcc_run2       12         4
## 60                       Approach=~BWin_v_Neut_L_NAcc_run2       12         5
## 61                       Approach=~BWin_v_Neut_R_NAcc_run2       13         1
## 62                       Approach=~BWin_v_Neut_R_NAcc_run2       13         2
## 63                       Approach=~BWin_v_Neut_R_NAcc_run2       13         3
## 64                       Approach=~BWin_v_Neut_R_NAcc_run2       13         4
## 65                       Approach=~BWin_v_Neut_R_NAcc_run2       13         5
## 66                     Approach=~BWin_v_Neut_R_Insula_run2       14         1
## 67                     Approach=~BWin_v_Neut_R_Insula_run2       14         2
## 68                     Approach=~BWin_v_Neut_R_Insula_run2       14         3
## 69                     Approach=~BWin_v_Neut_R_Insula_run2       14         4
## 70                     Approach=~BWin_v_Neut_R_Insula_run2       14         5
## 71                      Approach=~BWin_v_BLose_L_NAcc_run2       15         1
## 72                      Approach=~BWin_v_BLose_L_NAcc_run2       15         2
## 73                      Approach=~BWin_v_BLose_L_NAcc_run2       15         3
## 74                      Approach=~BWin_v_BLose_L_NAcc_run2       15         4
## 75                      Approach=~BWin_v_BLose_L_NAcc_run2       15         5
## 76                      Approach=~BWin_v_BLose_R_NAcc_run2       16         1
## 77                      Approach=~BWin_v_BLose_R_NAcc_run2       16         2
## 78                      Approach=~BWin_v_BLose_R_NAcc_run2       16         3
## 79                      Approach=~BWin_v_BLose_R_NAcc_run2       16         4
## 80                      Approach=~BWin_v_BLose_R_NAcc_run2       16         5
## 81                       Avoid=~ALose_v_Neut_L_Insula_run1       17         1
## 82                       Avoid=~ALose_v_Neut_L_Insula_run1       17         2
## 83                       Avoid=~ALose_v_Neut_L_Insula_run1       17         3
## 84                       Avoid=~ALose_v_Neut_L_Insula_run1       17         4
## 85                       Avoid=~ALose_v_Neut_L_Insula_run1       17         5
## 86                       Avoid=~BLose_v_Neut_L_Insula_run1       18         1
## 87                       Avoid=~BLose_v_Neut_L_Insula_run1       18         2
## 88                       Avoid=~BLose_v_Neut_L_Insula_run1       18         3
## 89                       Avoid=~BLose_v_Neut_L_Insula_run1       18         4
## 90                       Avoid=~BLose_v_Neut_L_Insula_run1       18         5
## 91                       Avoid=~BLose_v_Neut_R_Insula_run1       19         1
## 92                       Avoid=~BLose_v_Neut_R_Insula_run1       19         2
## 93                       Avoid=~BLose_v_Neut_R_Insula_run1       19         3
## 94                       Avoid=~BLose_v_Neut_R_Insula_run1       19         4
## 95                       Avoid=~BLose_v_Neut_R_Insula_run1       19         5
## 96                       Avoid=~BLose_v_BWin_L_Insula_run1       20         1
## 97                       Avoid=~BLose_v_BWin_L_Insula_run1       20         2
## 98                       Avoid=~BLose_v_BWin_L_Insula_run1       20         3
## 99                       Avoid=~BLose_v_BWin_L_Insula_run1       20         4
## 100                      Avoid=~BLose_v_BWin_L_Insula_run1       20         5
## 101                      Avoid=~BLose_v_BWin_R_Insula_run1       21         1
## 102                      Avoid=~BLose_v_BWin_R_Insula_run1       21         2
## 103                      Avoid=~BLose_v_BWin_R_Insula_run1       21         3
## 104                      Avoid=~BLose_v_BWin_R_Insula_run1       21         4
## 105                      Avoid=~BLose_v_BWin_R_Insula_run1       21         5
## 106                      Avoid=~ALose_v_Neut_L_Insula_run2       22         1
## 107                      Avoid=~ALose_v_Neut_L_Insula_run2       22         2
## 108                      Avoid=~ALose_v_Neut_L_Insula_run2       22         3
## 109                      Avoid=~ALose_v_Neut_L_Insula_run2       22         4
## 110                      Avoid=~ALose_v_Neut_L_Insula_run2       22         5
## 111                      Avoid=~ALose_v_Neut_R_Insula_run2       23         1
## 112                      Avoid=~ALose_v_Neut_R_Insula_run2       23         2
## 113                      Avoid=~ALose_v_Neut_R_Insula_run2       23         3
## 114                      Avoid=~ALose_v_Neut_R_Insula_run2       23         4
## 115                      Avoid=~ALose_v_Neut_R_Insula_run2       23         5
## 116                      Avoid=~BLose_v_Neut_L_Insula_run2       24         1
## 117                      Avoid=~BLose_v_Neut_L_Insula_run2       24         2
## 118                      Avoid=~BLose_v_Neut_L_Insula_run2       24         3
## 119                      Avoid=~BLose_v_Neut_L_Insula_run2       24         4
## 120                      Avoid=~BLose_v_Neut_L_Insula_run2       24         5
## 121                      Avoid=~BLose_v_Neut_R_Insula_run2       25         1
## 122                      Avoid=~BLose_v_Neut_R_Insula_run2       25         2
## 123                      Avoid=~BLose_v_Neut_R_Insula_run2       25         3
## 124                      Avoid=~BLose_v_Neut_R_Insula_run2       25         4
## 125                      Avoid=~BLose_v_Neut_R_Insula_run2       25         5
## 126                      Avoid=~BLose_v_BWin_L_Insula_run2       26         1
## 127                      Avoid=~BLose_v_BWin_L_Insula_run2       26         2
## 128                      Avoid=~BLose_v_BWin_L_Insula_run2       26         3
## 129                      Avoid=~BLose_v_BWin_L_Insula_run2       26         4
## 130                      Avoid=~BLose_v_BWin_L_Insula_run2       26         5
## 131                      Avoid=~BLose_v_BWin_R_Insula_run2       27         1
## 132                      Avoid=~BLose_v_BWin_R_Insula_run2       27         2
## 133                      Avoid=~BLose_v_BWin_R_Insula_run2       27         3
## 134                      Avoid=~BLose_v_BWin_R_Insula_run2       27         4
## 135                      Avoid=~BLose_v_BWin_R_Insula_run2       27         5
## 136       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       28         1
## 137       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       28         2
## 138       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       28         3
## 139       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       28         4
## 140       AWin_v_Neut_L_NAcc_run1~~AWin_v_Neut_L_NAcc_run1       28         5
## 141       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       29         1
## 142       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       29         2
## 143       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       29         3
## 144       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       29         4
## 145       AWin_v_Neut_R_NAcc_run1~~AWin_v_Neut_R_NAcc_run1       29         5
## 146   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       30         1
## 147   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       30         2
## 148   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       30         3
## 149   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       30         4
## 150   AWin_v_Neut_R_Insula_run1~~AWin_v_Neut_R_Insula_run1       30         5
## 151       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       31         1
## 152       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       31         2
## 153       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       31         3
## 154       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       31         4
## 155       BWin_v_Neut_L_NAcc_run1~~BWin_v_Neut_L_NAcc_run1       31         5
## 156       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       32         1
## 157       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       32         2
## 158       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       32         3
## 159       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       32         4
## 160       BWin_v_Neut_R_NAcc_run1~~BWin_v_Neut_R_NAcc_run1       32         5
## 161   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       33         1
## 162   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       33         2
## 163   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       33         3
## 164   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       33         4
## 165   BWin_v_Neut_R_Insula_run1~~BWin_v_Neut_R_Insula_run1       33         5
## 166     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       34         1
## 167     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       34         2
## 168     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       34         3
## 169     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       34         4
## 170     BWin_v_BLose_L_NAcc_run1~~BWin_v_BLose_L_NAcc_run1       34         5
## 171     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       35         1
## 172     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       35         2
## 173     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       35         3
## 174     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       35         4
## 175     BWin_v_BLose_R_NAcc_run1~~BWin_v_BLose_R_NAcc_run1       35         5
## 176       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       36         1
## 177       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       36         2
## 178       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       36         3
## 179       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       36         4
## 180       AWin_v_Neut_L_NAcc_run2~~AWin_v_Neut_L_NAcc_run2       36         5
## 181       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       37         1
## 182       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       37         2
## 183       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       37         3
## 184       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       37         4
## 185       AWin_v_Neut_R_NAcc_run2~~AWin_v_Neut_R_NAcc_run2       37         5
## 186   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       38         1
## 187   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       38         2
## 188   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       38         3
## 189   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       38         4
## 190   AWin_v_Neut_R_Insula_run2~~AWin_v_Neut_R_Insula_run2       38         5
## 191       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       39         1
## 192       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       39         2
## 193       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       39         3
## 194       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       39         4
## 195       BWin_v_Neut_L_NAcc_run2~~BWin_v_Neut_L_NAcc_run2       39         5
## 196       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       40         1
## 197       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       40         2
## 198       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       40         3
## 199       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       40         4
## 200       BWin_v_Neut_R_NAcc_run2~~BWin_v_Neut_R_NAcc_run2       40         5
## 201   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       41         1
## 202   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       41         2
## 203   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       41         3
## 204   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       41         4
## 205   BWin_v_Neut_R_Insula_run2~~BWin_v_Neut_R_Insula_run2       41         5
## 206     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       42         1
## 207     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       42         2
## 208     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       42         3
## 209     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       42         4
## 210     BWin_v_BLose_L_NAcc_run2~~BWin_v_BLose_L_NAcc_run2       42         5
## 211     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       43         1
## 212     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       43         2
## 213     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       43         3
## 214     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       43         4
## 215     BWin_v_BLose_R_NAcc_run2~~BWin_v_BLose_R_NAcc_run2       43         5
## 216 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       44         1
## 217 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       44         2
## 218 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       44         3
## 219 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       44         4
## 220 ALose_v_Neut_L_Insula_run1~~ALose_v_Neut_L_Insula_run1       44         5
## 221 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       45         1
## 222 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       45         2
## 223 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       45         3
## 224 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       45         4
## 225 BLose_v_Neut_L_Insula_run1~~BLose_v_Neut_L_Insula_run1       45         5
## 226 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       46         1
## 227 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       46         2
## 228 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       46         3
## 229 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       46         4
## 230 BLose_v_Neut_R_Insula_run1~~BLose_v_Neut_R_Insula_run1       46         5
## 231 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       47         1
## 232 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       47         2
## 233 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       47         3
## 234 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       47         4
## 235 BLose_v_BWin_L_Insula_run1~~BLose_v_BWin_L_Insula_run1       47         5
## 236 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       48         1
## 237 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       48         2
## 238 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       48         3
## 239 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       48         4
## 240 BLose_v_BWin_R_Insula_run1~~BLose_v_BWin_R_Insula_run1       48         5
## 241 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       49         1
## 242 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       49         2
## 243 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       49         3
## 244 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       49         4
## 245 ALose_v_Neut_L_Insula_run2~~ALose_v_Neut_L_Insula_run2       49         5
## 246 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       50         1
## 247 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       50         2
## 248 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       50         3
## 249 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       50         4
## 250 ALose_v_Neut_R_Insula_run2~~ALose_v_Neut_R_Insula_run2       50         5
## 251 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         1
## 252 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         2
## 253 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         3
## 254 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         4
## 255 BLose_v_Neut_L_Insula_run2~~BLose_v_Neut_L_Insula_run2       51         5
## 256 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         1
## 257 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         2
## 258 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         3
## 259 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         4
## 260 BLose_v_Neut_R_Insula_run2~~BLose_v_Neut_R_Insula_run2       52         5
## 261 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       53         1
## 262 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       53         2
## 263 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       53         3
## 264 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       53         4
## 265 BLose_v_BWin_L_Insula_run2~~BLose_v_BWin_L_Insula_run2       53         5
## 266 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       54         1
## 267 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       54         2
## 268 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       54         3
## 269 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       54         4
## 270 BLose_v_BWin_R_Insula_run2~~BLose_v_BWin_R_Insula_run2       54         5
## 271                                     Approach~~Approach       55         1
## 272                                     Approach~~Approach       55         2
## 273                                     Approach~~Approach       55         3
## 274                                     Approach~~Approach       55         4
## 275                                     Approach~~Approach       55         5
## 276                                           Avoid~~Avoid       56         1
## 277                                           Avoid~~Avoid       56         2
## 278                                           Avoid~~Avoid       56         3
## 279                                           Avoid~~Avoid       56         4
## 280                                           Avoid~~Avoid       56         5
## 281                                        Approach~~Avoid       57         1
## 282                                        Approach~~Avoid       57         2
## 283                                        Approach~~Avoid       57         3
## 284                                        Approach~~Avoid       57         4
## 285                                        Approach~~Avoid       57         5
## 286                              AWin_v_Neut_L_NAcc_run1~1       58         1
## 287                              AWin_v_Neut_L_NAcc_run1~1       58         2
## 288                              AWin_v_Neut_L_NAcc_run1~1       58         3
## 289                              AWin_v_Neut_L_NAcc_run1~1       58         4
## 290                              AWin_v_Neut_L_NAcc_run1~1       58         5
## 291                              AWin_v_Neut_R_NAcc_run1~1       59         1
## 292                              AWin_v_Neut_R_NAcc_run1~1       59         2
## 293                              AWin_v_Neut_R_NAcc_run1~1       59         3
## 294                              AWin_v_Neut_R_NAcc_run1~1       59         4
## 295                              AWin_v_Neut_R_NAcc_run1~1       59         5
## 296                            AWin_v_Neut_R_Insula_run1~1       60         1
## 297                            AWin_v_Neut_R_Insula_run1~1       60         2
## 298                            AWin_v_Neut_R_Insula_run1~1       60         3
## 299                            AWin_v_Neut_R_Insula_run1~1       60         4
## 300                            AWin_v_Neut_R_Insula_run1~1       60         5
## 301                              BWin_v_Neut_L_NAcc_run1~1       61         1
## 302                              BWin_v_Neut_L_NAcc_run1~1       61         2
## 303                              BWin_v_Neut_L_NAcc_run1~1       61         3
## 304                              BWin_v_Neut_L_NAcc_run1~1       61         4
## 305                              BWin_v_Neut_L_NAcc_run1~1       61         5
## 306                              BWin_v_Neut_R_NAcc_run1~1       62         1
## 307                              BWin_v_Neut_R_NAcc_run1~1       62         2
## 308                              BWin_v_Neut_R_NAcc_run1~1       62         3
## 309                              BWin_v_Neut_R_NAcc_run1~1       62         4
## 310                              BWin_v_Neut_R_NAcc_run1~1       62         5
## 311                            BWin_v_Neut_R_Insula_run1~1       63         1
## 312                            BWin_v_Neut_R_Insula_run1~1       63         2
## 313                            BWin_v_Neut_R_Insula_run1~1       63         3
## 314                            BWin_v_Neut_R_Insula_run1~1       63         4
## 315                            BWin_v_Neut_R_Insula_run1~1       63         5
## 316                             BWin_v_BLose_L_NAcc_run1~1       64         1
## 317                             BWin_v_BLose_L_NAcc_run1~1       64         2
## 318                             BWin_v_BLose_L_NAcc_run1~1       64         3
## 319                             BWin_v_BLose_L_NAcc_run1~1       64         4
## 320                             BWin_v_BLose_L_NAcc_run1~1       64         5
## 321                             BWin_v_BLose_R_NAcc_run1~1       65         1
## 322                             BWin_v_BLose_R_NAcc_run1~1       65         2
## 323                             BWin_v_BLose_R_NAcc_run1~1       65         3
## 324                             BWin_v_BLose_R_NAcc_run1~1       65         4
## 325                             BWin_v_BLose_R_NAcc_run1~1       65         5
## 326                              AWin_v_Neut_L_NAcc_run2~1       66         1
## 327                              AWin_v_Neut_L_NAcc_run2~1       66         2
## 328                              AWin_v_Neut_L_NAcc_run2~1       66         3
## 329                              AWin_v_Neut_L_NAcc_run2~1       66         4
## 330                              AWin_v_Neut_L_NAcc_run2~1       66         5
## 331                              AWin_v_Neut_R_NAcc_run2~1       67         1
## 332                              AWin_v_Neut_R_NAcc_run2~1       67         2
## 333                              AWin_v_Neut_R_NAcc_run2~1       67         3
## 334                              AWin_v_Neut_R_NAcc_run2~1       67         4
## 335                              AWin_v_Neut_R_NAcc_run2~1       67         5
## 336                            AWin_v_Neut_R_Insula_run2~1       68         1
## 337                            AWin_v_Neut_R_Insula_run2~1       68         2
## 338                            AWin_v_Neut_R_Insula_run2~1       68         3
## 339                            AWin_v_Neut_R_Insula_run2~1       68         4
## 340                            AWin_v_Neut_R_Insula_run2~1       68         5
## 341                              BWin_v_Neut_L_NAcc_run2~1       69         1
## 342                              BWin_v_Neut_L_NAcc_run2~1       69         2
## 343                              BWin_v_Neut_L_NAcc_run2~1       69         3
## 344                              BWin_v_Neut_L_NAcc_run2~1       69         4
## 345                              BWin_v_Neut_L_NAcc_run2~1       69         5
## 346                              BWin_v_Neut_R_NAcc_run2~1       70         1
## 347                              BWin_v_Neut_R_NAcc_run2~1       70         2
## 348                              BWin_v_Neut_R_NAcc_run2~1       70         3
## 349                              BWin_v_Neut_R_NAcc_run2~1       70         4
## 350                              BWin_v_Neut_R_NAcc_run2~1       70         5
## 351                            BWin_v_Neut_R_Insula_run2~1       71         1
## 352                            BWin_v_Neut_R_Insula_run2~1       71         2
## 353                            BWin_v_Neut_R_Insula_run2~1       71         3
## 354                            BWin_v_Neut_R_Insula_run2~1       71         4
## 355                            BWin_v_Neut_R_Insula_run2~1       71         5
## 356                             BWin_v_BLose_L_NAcc_run2~1       72         1
## 357                             BWin_v_BLose_L_NAcc_run2~1       72         2
## 358                             BWin_v_BLose_L_NAcc_run2~1       72         3
## 359                             BWin_v_BLose_L_NAcc_run2~1       72         4
## 360                             BWin_v_BLose_L_NAcc_run2~1       72         5
## 361                             BWin_v_BLose_R_NAcc_run2~1       73         1
## 362                             BWin_v_BLose_R_NAcc_run2~1       73         2
## 363                             BWin_v_BLose_R_NAcc_run2~1       73         3
## 364                             BWin_v_BLose_R_NAcc_run2~1       73         4
## 365                             BWin_v_BLose_R_NAcc_run2~1       73         5
## 366                           ALose_v_Neut_L_Insula_run1~1       74         1
## 367                           ALose_v_Neut_L_Insula_run1~1       74         2
## 368                           ALose_v_Neut_L_Insula_run1~1       74         3
## 369                           ALose_v_Neut_L_Insula_run1~1       74         4
## 370                           ALose_v_Neut_L_Insula_run1~1       74         5
## 371                           BLose_v_Neut_L_Insula_run1~1       75         1
## 372                           BLose_v_Neut_L_Insula_run1~1       75         2
## 373                           BLose_v_Neut_L_Insula_run1~1       75         3
## 374                           BLose_v_Neut_L_Insula_run1~1       75         4
## 375                           BLose_v_Neut_L_Insula_run1~1       75         5
## 376                           BLose_v_Neut_R_Insula_run1~1       76         1
## 377                           BLose_v_Neut_R_Insula_run1~1       76         2
## 378                           BLose_v_Neut_R_Insula_run1~1       76         3
## 379                           BLose_v_Neut_R_Insula_run1~1       76         4
## 380                           BLose_v_Neut_R_Insula_run1~1       76         5
## 381                           BLose_v_BWin_L_Insula_run1~1       77         1
## 382                           BLose_v_BWin_L_Insula_run1~1       77         2
## 383                           BLose_v_BWin_L_Insula_run1~1       77         3
## 384                           BLose_v_BWin_L_Insula_run1~1       77         4
## 385                           BLose_v_BWin_L_Insula_run1~1       77         5
## 386                           BLose_v_BWin_R_Insula_run1~1       78         1
## 387                           BLose_v_BWin_R_Insula_run1~1       78         2
## 388                           BLose_v_BWin_R_Insula_run1~1       78         3
## 389                           BLose_v_BWin_R_Insula_run1~1       78         4
## 390                           BLose_v_BWin_R_Insula_run1~1       78         5
## 391                           ALose_v_Neut_L_Insula_run2~1       79         1
## 392                           ALose_v_Neut_L_Insula_run2~1       79         2
## 393                           ALose_v_Neut_L_Insula_run2~1       79         3
## 394                           ALose_v_Neut_L_Insula_run2~1       79         4
## 395                           ALose_v_Neut_L_Insula_run2~1       79         5
## 396                           ALose_v_Neut_R_Insula_run2~1       80         1
## 397                           ALose_v_Neut_R_Insula_run2~1       80         2
## 398                           ALose_v_Neut_R_Insula_run2~1       80         3
## 399                           ALose_v_Neut_R_Insula_run2~1       80         4
## 400                           ALose_v_Neut_R_Insula_run2~1       80         5
## 401                           BLose_v_Neut_L_Insula_run2~1       81         1
## 402                           BLose_v_Neut_L_Insula_run2~1       81         2
## 403                           BLose_v_Neut_L_Insula_run2~1       81         3
## 404                           BLose_v_Neut_L_Insula_run2~1       81         4
## 405                           BLose_v_Neut_L_Insula_run2~1       81         5
## 406                           BLose_v_Neut_R_Insula_run2~1       82         1
## 407                           BLose_v_Neut_R_Insula_run2~1       82         2
## 408                           BLose_v_Neut_R_Insula_run2~1       82         3
## 409                           BLose_v_Neut_R_Insula_run2~1       82         4
## 410                           BLose_v_Neut_R_Insula_run2~1       82         5
## 411                           BLose_v_BWin_L_Insula_run2~1       83         1
## 412                           BLose_v_BWin_L_Insula_run2~1       83         2
## 413                           BLose_v_BWin_L_Insula_run2~1       83         3
## 414                           BLose_v_BWin_L_Insula_run2~1       83         4
## 415                           BLose_v_BWin_L_Insula_run2~1       83         5
## 416                           BLose_v_BWin_R_Insula_run2~1       84         1
## 417                           BLose_v_BWin_R_Insula_run2~1       84         2
## 418                           BLose_v_BWin_R_Insula_run2~1       84         3
## 419                           BLose_v_BWin_R_Insula_run2~1       84         4
## 420                           BLose_v_BWin_R_Insula_run2~1       84         5
## 421                                             Approach~1       85         1
## 422                                             Approach~1       85         2
## 423                                             Approach~1       85         3
## 424                                             Approach~1       85         4
## 425                                             Approach~1       85         5
## 426                                                Avoid~1       86         1
## 427                                                Avoid~1       86         2
## 428                                                Avoid~1       86         3
## 429                                                Avoid~1       86         4
## 430                                                Avoid~1       86         5
## 431                                                  rmsea       87         1
## 432                                                  rmsea       87         2
## 433                                                  rmsea       87         3
## 434                                                  rmsea       87         4
## 435                                                  rmsea       87         5
## 436                                                    cfi       88         1
## 437                                                    cfi       88         2
## 438                                                    cfi       88         3
## 439                                                    cfi       88         4
## 440                                                    cfi       88         5
## 441                                                    tli       89         1
## 442                                                    tli       89         2
## 443                                                    tli       89         3
## 444                                                    tli       89         4
## 445                                                    tli       89         5
## 446                                                    gfi       90         1
## 447                                                    gfi       90         2
## 448                                                    gfi       90         3
## 449                                                    gfi       90         4
## 450                                                    gfi       90         5
## 451                                                   srmr       91         1
## 452                                                   srmr       91         2
## 453                                                   srmr       91         3
## 454                                                   srmr       91         4
## 455                                                   srmr       91         5
##        est   p
## 1   -0.017 0.4
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## 3    0.005 0.8
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